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Johannes Gutenberg Universität Mainz
1.
Griesmaier, Roland.
Detection of small buried objects: asymptotic factorization and MUSIC.
Degree: 2008, Johannes Gutenberg Universität Mainz
URL: http://ubm.opus.hbz-nrw.de/volltexte/2008/1666/ 
► In this work, we consider a simple model problem for the electromagnetic exploration of small perfectly conducting objects buried within the lower halfspace of an…
(more)
▼ In this work, we consider a simple model problem for the electromagnetic exploration of small perfectly conducting objects buried within the lower halfspace of an unbounded two–layered background medium. In possible applications, such as, e.g., humanitarian demining, the two layers would correspond to air and soil. Moving a set of electric devices parallel to the surface of ground to generate a time–harmonic field, the induced field is measured within the same devices. The goal is to retrieve information about buried scatterers from these data.
In mathematical terms, we are concerned with the analysis and numerical solution of the inverse scattering problem to reconstruct the number and the positions of a collection of finitely many small perfectly conducting scatterers buried within the lower halfspace of an unbounded two–layered background medium from near field measurements of time–harmonic electromagnetic waves.
For this purpose, we first study the corresponding direct scattering problem in detail and derive an asymptotic expansion of the scattered field as the size of the scatterers tends to zero. Then, we use this expansion to justify a noniterative MUSIC–type reconstruction method for the solution of the inverse scattering problem. We propose a numerical implementation of this reconstruction method and provide a series of numerical experiments.
In der vorliegenden Arbeit behandeln wir ein einfaches Modell für die Lokalisierung kleiner perfekt leitender unter der Erdoberfläche vergrabener Objekte mit Hilfe zeitharmonischer elektromagnetischer Wellen. Dazu betrachten wir ein unbeschränktes Zweischichtmedium (oben Luft/unten Erde) mit ebener Trennschicht und erzeugen mit Hilfe geeigneter Messgeräte,
die parallel zur Trennschicht im oberen Halbraum angeordnet sein sollen, elektromagnetische Felder. Diese Felder werden an im unteren Halbraum vergrabenen Objekten gestreut, und das resultierende Streufeld wird wiederum mit obengenannten Messgeräten gemessen. Das Ziel ist, aus diesen Daten Informationen über im Boden vergrabene Objekte zu gewinnen.
Mathematisch formuliert, beschäftigen wir uns mit der Analyse und
der numerischen Lösung des inversen Streuproblems die Anzahl und die Positionen endlich vieler kleiner perfekt leitender Streukörper, die im unteren Halbraum eines Zweischichtmediums vergraben sind, aus Nahfeldmessungen elektromagnetischer Felder zu bestimmen.
Dazu untersuchen wir zuerst das zugehörige direkte Streuproblem und beweisen mit Hilfe von Integralgleichungsmethoden anhand einer Faktorisierung des Nahfeldmessoperators eine asymptotische Entwicklung des Streufeldes für kleine Streukörper. Anschließend verwenden wir diese Entwicklung, um ein nichtiteratives Rekonstruktionsverfahren, das der Klasse der MUSIC-Verfahren zuzuordnen ist, theoretisch zu fundieren. Wir schlagen eine numerische Implementierung dieses Verfahrens vor und präsentieren ein Reihe von numerischen Ergebnissen, die unsere theoretischen Resultate bestätigen.
Subjects/Keywords: Inverse Probleme; inverse problems; Mathematics
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APA (6th Edition):
Griesmaier, R. (2008). Detection of small buried objects: asymptotic factorization and MUSIC. (Doctoral Dissertation). Johannes Gutenberg Universität Mainz. Retrieved from http://ubm.opus.hbz-nrw.de/volltexte/2008/1666/
Chicago Manual of Style (16th Edition):
Griesmaier, Roland. “Detection of small buried objects: asymptotic factorization and MUSIC.” 2008. Doctoral Dissertation, Johannes Gutenberg Universität Mainz. Accessed March 01, 2021.
http://ubm.opus.hbz-nrw.de/volltexte/2008/1666/.
MLA Handbook (7th Edition):
Griesmaier, Roland. “Detection of small buried objects: asymptotic factorization and MUSIC.” 2008. Web. 01 Mar 2021.
Vancouver:
Griesmaier R. Detection of small buried objects: asymptotic factorization and MUSIC. [Internet] [Doctoral dissertation]. Johannes Gutenberg Universität Mainz; 2008. [cited 2021 Mar 01].
Available from: http://ubm.opus.hbz-nrw.de/volltexte/2008/1666/.
Council of Science Editors:
Griesmaier R. Detection of small buried objects: asymptotic factorization and MUSIC. [Doctoral Dissertation]. Johannes Gutenberg Universität Mainz; 2008. Available from: http://ubm.opus.hbz-nrw.de/volltexte/2008/1666/
2.
Le, Ellen Brooke.
Data-driven reduction strategies for Bayesian inverse problems.
Degree: PhD, Computational Science, Engineering, and Mathematics, 2018, University of Texas – Austin
URL: http://hdl.handle.net/2152/65851
► A persistent central challenge in computational science and engineering (CSE), with both national and global security implications, is the efficient solution of large-scale Bayesian inverse…
(more)
▼ A persistent central challenge in computational science and engineering (CSE), with both national and global security implications, is the efficient solution of large-scale Bayesian
inverse problems. These
problems range from estimating material parameters in subsurface simulations to estimating phenomenological parameters in climate models. Despite recent progress, our ability to quantify uncertainties and solve large-scale
inverse problems lags well behind our ability to develop the governing forward simulations.
Inverse problems present unique computational challenges that are only magnified as we include larger observational data sets and demand higher-resolution parameter estimates. Even with the current state-of-the-art, solving deterministic large-scale
inverse problems is prohibitively expensive. Large-scale uncertainty quantification (UQ), cast in the Bayesian inversion framework, is thus rendered intractable. To conquer these challenges, new methods that target the root causes of computational complexity are needed.
In this dissertation, we propose data-driven strategies for overcoming this “curse of di- mensionality.” First, we address the computational complexity induced in large-scale
inverse problems by high-dimensional observational data. We propose a randomized misfit approach
(RMA), which uses random projections—quasi-orthogonal, information-preserving transformations—to map the high-dimensional data-misfit vector to a low-dimensional space. We provide the first theoretical explanation for why randomized misfit methods are successful in practice with a small reduced data-misfit dimension (n = O(1)).
Next, we develop the randomized geostatistical approach (RGA) for Bayesian sub- surface
inverse problems with high-dimensional data. We show that the RGA is able to resolve transient groundwater
inverse problems with noisy observed data dimensions up to 107, whereas a comparison method fails due to out-of-memory errors.
Finally, we address the solution of Bayesian
inverse problems with spatially localized data. The motivation is CSE applications that would gain from high-fidelity estimation over a smaller data-local domain, versus expensive and uncertain estimation over the full simulation domain. We propose several truncated domain inversion methods using domain decomposition theory to build model-informed artificial boundary conditions. Numerical investigations of MAP estimation and sampling demonstrate improved fidelity and fewer partial differential equation (PDE) solves with our truncated methods.
Advisors/Committee Members: Bui-Thanh, Tan (advisor), Nguyen, Quoc P. (advisor), Oden, J Tinsley T (committee member), Ward, Rachel A (committee member), Ghattas, Omar (committee member).
Subjects/Keywords: Bayesian inverse problems
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APA (6th Edition):
Le, E. B. (2018). Data-driven reduction strategies for Bayesian inverse problems. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/65851
Chicago Manual of Style (16th Edition):
Le, Ellen Brooke. “Data-driven reduction strategies for Bayesian inverse problems.” 2018. Doctoral Dissertation, University of Texas – Austin. Accessed March 01, 2021.
http://hdl.handle.net/2152/65851.
MLA Handbook (7th Edition):
Le, Ellen Brooke. “Data-driven reduction strategies for Bayesian inverse problems.” 2018. Web. 01 Mar 2021.
Vancouver:
Le EB. Data-driven reduction strategies for Bayesian inverse problems. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2018. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/2152/65851.
Council of Science Editors:
Le EB. Data-driven reduction strategies for Bayesian inverse problems. [Doctoral Dissertation]. University of Texas – Austin; 2018. Available from: http://hdl.handle.net/2152/65851
NSYSU
3.
Wang, Wei-Chuan.
Direct and inverse problems for one-dimensional p-Laplacian operators.
Degree: PhD, Applied Mathematics, 2010, NSYSU
URL: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0531110-195414
► In this thesis, direct and inverse problems concerning nodal solutions associated with the one-dimensional p-Laplacian operators are studied. We first consider the eigenvalue problem on…
(more)
▼ In this thesis, direct and
inverse problems concerning nodal solutions associated with the one-dimensional p-Laplacian operators are studied. We first consider the eigenvalue
problem on (0, 1),
−(y0(p−1))0 + (p − 1)q(x)y(p−1) = (p − 1) λw(x)y(p−1) (0.1)
Here f(p−1) := |f|p−2f = |f|p−1 sgn f. This problem, though nonlinear and degenerate, behaves very similar to the classical Sturm-Liouville problem, which is the special case
p = 2. The spectrum {λk} of the problem coupled with linear separated boundary conditions are discrete and the eigenfunction yn corresponding toλn has exactly n−1 zeros in (0, 1). Using a Prâ¥ufer-type substitution and properties of the generalized sine function, Sp(x), we solve the reconstruction and stablity issues of the
inverse nodal
problems for Dirichlet boundary conditions, as well as periodic/antiperiodic boundary conditions whenever w(x) λ 1. Corresponding Ambarzumyan
problems are also solved.
We also study an associated boundary value problem with a nonlinear nonhomogeneous
term (p−1)w(x) f(y(x)) on the right hand side of (0.1), where w is continuously differentiable and positive, q is continuously differentiable and f is positive and Lipschitz
continuous on R+, and odd on R such that
f0 := lim
y!0+
f(y)
yp−1 , f1 := lim
y!1
f(y)
yp−1 .
are not equal. We extend Kongâs results for p = 2 to general p > 1, which states that whenever an eigenvalue _n 2 (f0, f1) or (f1, f0), there exists a nodal solution un
having exactly n − 1 zeros in (0, 1), for the above nonhomogeneous equation equipped
with any linear separated boundary conditions.
Although it is known that there are indeed some differences, Our results show that the one-dimensional p-Laplacian operator is still very similar to the Sturm-Liouville operator, in aspects involving Prâ¥ufer substitution techniques.
Advisors/Committee Members: Chun-Kong Law (committee member), Chao-Nien Chen (chair), Wei-Cheng Lian (chair).
Subjects/Keywords: p-Laplacian; inverse problems
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APA (6th Edition):
Wang, W. (2010). Direct and inverse problems for one-dimensional p-Laplacian operators. (Doctoral Dissertation). NSYSU. Retrieved from http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0531110-195414
Chicago Manual of Style (16th Edition):
Wang, Wei-Chuan. “Direct and inverse problems for one-dimensional p-Laplacian operators.” 2010. Doctoral Dissertation, NSYSU. Accessed March 01, 2021.
http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0531110-195414.
MLA Handbook (7th Edition):
Wang, Wei-Chuan. “Direct and inverse problems for one-dimensional p-Laplacian operators.” 2010. Web. 01 Mar 2021.
Vancouver:
Wang W. Direct and inverse problems for one-dimensional p-Laplacian operators. [Internet] [Doctoral dissertation]. NSYSU; 2010. [cited 2021 Mar 01].
Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0531110-195414.
Council of Science Editors:
Wang W. Direct and inverse problems for one-dimensional p-Laplacian operators. [Doctoral Dissertation]. NSYSU; 2010. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0531110-195414
Cornell University
4.
Sabelli, Anthony.
Novel Methods For Source Localization And Material Identification.
Degree: PhD, Applied Mathematics, 2013, Cornell University
URL: http://hdl.handle.net/1813/33808
► In this work we present two independent inverse problem methods. In the first chapter we address the problem of source localization. Localizing sources in physical…
(more)
▼ In this work we present two independent
inverse problem methods. In the first chapter we address the problem of source localization. Localizing sources in physical systems represents a class of
inverse problems with broad scientific and engineering applications. This chapter is concerned with the development of a non-iterative source sensitivity approach for the localization of sources in linear systems under steady-state. We show that our proposed approach can be applied to a broad class of physical
problems, ranging from source localization in elastodynamics and acoustics to source detection in heat/mass transport
problems. The source sensitivity field introduced in this work represents the change of a cost functional caused by the appearance of an infinitesimal source is a given domain (or its boundary). In order to extract macroscopic inferences, we apply a threshold to the source sensitivity field in a way that parallels the application of the topological derivative concept in shape identification. We establish precise formulas for the source sensitivity field using a direct approach and a Lagrangian formulation. We show that computing the source sensitivity field entails just obtaining the solution of a single adjoint problem. Hence, the computational expense of obtaining the source sensitivity is of the same order as that of solving one forward problem. We illustrate the performance of the method through numerical examples drawn from the areas of elastodynamics, acoustics, and heat and mass transport. Our results show that our proposed approach could be used on its own as a source detection tool or to obtain initial guesses for more quantitative iterative gradient-based minimization strategies. In the second chapter we focus on material characterization. Material identification is integral to medical imaging, finite element calibration, non destructive testing, and other engineering applications. We propose an iterative computational framework for nonlinear material identification with transient data. Our method centers on the weak enforcement of the internal force computation, through which we derive a modified internal force equation. We subsequently enforce potentially sparse measurements in a least squares penalty term. The modified internal force equation results in a fully space-time coupled forward and adjoint problem. We consider two steps at each iteration. First the solution to the coupled problem, and second the material parameter update. Our approach generalizes the technique used for linear elastic materials. For our numerical examples, we focus on the Iwan constitutive model, commonly used to model frictional interactions in mechanical joints. We show several numerical examples exploring the accuracy of the coupled problem solution as well as the material reconstruction. We conclude with larger examples requiring distributed computation in order to demonstrate not only the algorithmic properties, but the computational scalability.
Advisors/Committee Members: Aquino, Wilkins (chair), Bindel, David S. (committee member), Vladimirsky, Alexander B. (committee member).
Subjects/Keywords: Inverse Problems; Computational Mechanics
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APA (6th Edition):
Sabelli, A. (2013). Novel Methods For Source Localization And Material Identification. (Doctoral Dissertation). Cornell University. Retrieved from http://hdl.handle.net/1813/33808
Chicago Manual of Style (16th Edition):
Sabelli, Anthony. “Novel Methods For Source Localization And Material Identification.” 2013. Doctoral Dissertation, Cornell University. Accessed March 01, 2021.
http://hdl.handle.net/1813/33808.
MLA Handbook (7th Edition):
Sabelli, Anthony. “Novel Methods For Source Localization And Material Identification.” 2013. Web. 01 Mar 2021.
Vancouver:
Sabelli A. Novel Methods For Source Localization And Material Identification. [Internet] [Doctoral dissertation]. Cornell University; 2013. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/1813/33808.
Council of Science Editors:
Sabelli A. Novel Methods For Source Localization And Material Identification. [Doctoral Dissertation]. Cornell University; 2013. Available from: http://hdl.handle.net/1813/33808
Cornell University
5.
Sternfels, Henri.
Geometric Tools, Sampling Strategies, Bayesian Inverse Problems And Design Under Uncertainty.
Degree: PhD, Civil and Environmental Engineering, 2013, Cornell University
URL: http://hdl.handle.net/1813/33860
► The main contributions of the present thesis are novel computational methods related to uncertainty quantification, inverse problems and reduced order modeling in engineering. In the…
(more)
▼ The main contributions of the present thesis are novel computational methods related to uncertainty quantification,
inverse problems and reduced order modeling in engineering. In the first chapter, we describe a framework to optimize an engineering system under large uncertainties. The optimization problem being recast as a sampling problem, the use of advanced sampling schemes associated with a hierarchical approach using approximate models enables an efficient identification of design values; along with corresponding sensitivity and robustness information. The second chapter deals with the solution of Bayesian
inverse problems, in which unknown parameter values in a model are being inferred from uncertain measurements of the output of the system of interest. A reduced order model interpolation scheme, based on differential geometric ideas, enables faster computations during the posterior sampling process while maintaining a high accuracy. Finally, the last chapter proposes a solution to the snapshot selection problem in reduced order modeling, namely how to select the parameters that represent best the system of interest in the parameter space. The approach chosen is to interpret the parameter space as a Riemannian manifold, with a sensitivity related metric emphasizing regions with more information. The numerical applications chosen for each of those
problems are engineering oriented, with the corresponding models being discretized using the finite element method.
Advisors/Committee Members: Earls, Christopher J (chair), Grigoriu, Mircea Dan (committee member), Van Loan, Charles Francis (committee member).
Subjects/Keywords: Uncertainty Quantification; Inverse Problems
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APA (6th Edition):
Sternfels, H. (2013). Geometric Tools, Sampling Strategies, Bayesian Inverse Problems And Design Under Uncertainty. (Doctoral Dissertation). Cornell University. Retrieved from http://hdl.handle.net/1813/33860
Chicago Manual of Style (16th Edition):
Sternfels, Henri. “Geometric Tools, Sampling Strategies, Bayesian Inverse Problems And Design Under Uncertainty.” 2013. Doctoral Dissertation, Cornell University. Accessed March 01, 2021.
http://hdl.handle.net/1813/33860.
MLA Handbook (7th Edition):
Sternfels, Henri. “Geometric Tools, Sampling Strategies, Bayesian Inverse Problems And Design Under Uncertainty.” 2013. Web. 01 Mar 2021.
Vancouver:
Sternfels H. Geometric Tools, Sampling Strategies, Bayesian Inverse Problems And Design Under Uncertainty. [Internet] [Doctoral dissertation]. Cornell University; 2013. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/1813/33860.
Council of Science Editors:
Sternfels H. Geometric Tools, Sampling Strategies, Bayesian Inverse Problems And Design Under Uncertainty. [Doctoral Dissertation]. Cornell University; 2013. Available from: http://hdl.handle.net/1813/33860
Texas A&M University
6.
Zhang, Zhidong.
Inverse Problems for Fractional Diffusion Equations.
Degree: PhD, Mathematics, 2017, Texas A&M University
URL: http://hdl.handle.net/1969.1/165701
► By Fick’s laws of diffusion, in the classical diffusion process, the mean square path ‹x2› is proportional to the time t as t →∞,. However,…
(more)
▼ By Fick’s laws of diffusion, in the classical diffusion process, the mean square path ‹x2› is proportional to the time t as t →∞,. However, in practice, some anomalous diffusion processes may occur, in which the relation ‹x2› t, ≠ 1 holds. To describe such processes, we need to add the fractional derivative on the time t, which forms the fractional diffusion equation, and we call it FDE for short.
This dissertation contains some
inverse problems in FDEs. Specifically, the
recovery of unknown conditions of coefficients from additional data on the solution u will be considered. The results of fractional
inverse problems are totally different from the ones of the classical case. For instance, the degree of ill-posedness. This is due to the polynomial asymptotic behavior of the Mittag-Leffler function, which consists of the fundamental solution of FDE. This difference leads to new physics and we can ask a question that do similar things always occur? The short answer is not always and the slightly longer version is the analysis is always more complex. This makes the research on
inverse problems in FDEs both challenging and interesting.
For each
inverse problem in this dissertation, at first it was necessary to extend existing results about the direct problem, namely the situation where all parameters in the equation are known and we must recover u(x, t). This includes the existence, uniqueness and regularity estimates of the solution. Then for the
inverse problem, the initial step in many of these situations is to use the equation structure to obtain an operator K one of whose fixed points is the unknown function we seek. With this K; the key step is proving the monotonicity of the operator in a suitable partially ordered space and then showing uniqueness of its fixed points. In conclusion, the monotonicity property and the domain of the operator K will lead to an iterative reconstruction algorithm and some numerical results are reproduced to verify the theoretical conclusions.
Advisors/Committee Members: Rundell, William (advisor), Howard, Peter (committee member), Mukherjee, Partha (committee member), Zhou, Jianxin (committee member).
Subjects/Keywords: Inverse problems; fractional diffusion equations
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APA ·
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APA (6th Edition):
Zhang, Z. (2017). Inverse Problems for Fractional Diffusion Equations. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/165701
Chicago Manual of Style (16th Edition):
Zhang, Zhidong. “Inverse Problems for Fractional Diffusion Equations.” 2017. Doctoral Dissertation, Texas A&M University. Accessed March 01, 2021.
http://hdl.handle.net/1969.1/165701.
MLA Handbook (7th Edition):
Zhang, Zhidong. “Inverse Problems for Fractional Diffusion Equations.” 2017. Web. 01 Mar 2021.
Vancouver:
Zhang Z. Inverse Problems for Fractional Diffusion Equations. [Internet] [Doctoral dissertation]. Texas A&M University; 2017. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/1969.1/165701.
Council of Science Editors:
Zhang Z. Inverse Problems for Fractional Diffusion Equations. [Doctoral Dissertation]. Texas A&M University; 2017. Available from: http://hdl.handle.net/1969.1/165701
Queens University
7.
Milne, Tristan.
Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation
.
Degree: Mathematics and Statistics, 2016, Queens University
URL: http://hdl.handle.net/1974/14738
► We study the Dirichlet to Neumann operator for the Riemannian wave equation on a compact Riemannian manifold. If the Riemannian manifold is modelled as an…
(more)
▼ We study the Dirichlet to Neumann operator for the Riemannian wave equation on a compact Riemannian manifold. If the Riemannian manifold is modelled as an elastic medium, this operator represents the data available to an observer on the boundary of the manifold when the manifold is set into motion through boundary vibrations. We study the Dirichlet to Neumann operator when vibrations are imposed and data recorded on disjoint sets, a useful setting for applications. We prove that this operator determines the Dirichlet to Neumann operator where sources and observations are on the same set, provided a spectral condition on the Laplace-Beltrami operator for the manifold is satisfied. We prove this by providing an implementable procedure for determining a portion of the Riemannian manifold near the area where sources are applied. Drawing on established results, an immediate corollary is that a compact Riemannian manifold can be reconstructed from the Dirichlet to Neumann operator where sources and observations are on disjoint sets.
Subjects/Keywords: Partial Differential Equations
;
Inverse Problems
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APA (6th Edition):
Milne, T. (2016). Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation
. (Thesis). Queens University. Retrieved from http://hdl.handle.net/1974/14738
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Milne, Tristan. “Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation
.” 2016. Thesis, Queens University. Accessed March 01, 2021.
http://hdl.handle.net/1974/14738.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Milne, Tristan. “Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation
.” 2016. Web. 01 Mar 2021.
Vancouver:
Milne T. Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation
. [Internet] [Thesis]. Queens University; 2016. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/1974/14738.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Milne T. Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation
. [Thesis]. Queens University; 2016. Available from: http://hdl.handle.net/1974/14738
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Manchester
8.
Nugroho, Agung Tjahjo.
Microwave tomography.
Degree: PhD, 2016, University of Manchester
URL: https://www.research.manchester.ac.uk/portal/en/theses/microwave-tomography(1000bea8-f286-42dc-9def-8aa09411160e).html
;
http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.677742
► This thesis reports on the research carried out in the area of Microwave Tomography (MWT) where the study aims to develop inversion algorithms to obtain…
(more)
▼ This thesis reports on the research carried out in the area of Microwave Tomography (MWT) where the study aims to develop inversion algorithms to obtain cheap and stable solutions of MWT inverse scattering problems which are mathematically formulated as nonlinear ill posed problems. The study develops two algorithms namely Inexact Newton Backtracking Method (INBM) and Newton Iterative-Conjugate Gradient on Normal Equation (NI-CGNE) which are based on Newton method. These algorithms apply implicit solutions of the Newton equations with unspecific manner functioning as the regularized step size of the Newton iterative. The two developed methods were tested by the use of numerical examples and experimental data gained by the MWT system of the University of Manchester. The numerical experiments were done on samples with dielectric contrast objects containing different kinds of materials and lossy materials. Meanwhile, the quality of the methods is evaluated by comparingthem with the Levenberg Marquardt method (LM). Under the natural assumption that the INBM is a regularized method and the CGNE is a semi regularized method, the results of experiments show that INBM and NI-CGNE improve the speed, the spatial resolutions and the quality of direct regularization method by means of the LM method. The experiments also show that the developed algorithms are more flexible to theeffect of noise and lossy materials compared with the LM algorithm.
Subjects/Keywords: 621.381; Microwave Tomography; Inverse Problems
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APA ·
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MLA ·
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CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Nugroho, A. T. (2016). Microwave tomography. (Doctoral Dissertation). University of Manchester. Retrieved from https://www.research.manchester.ac.uk/portal/en/theses/microwave-tomography(1000bea8-f286-42dc-9def-8aa09411160e).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.677742
Chicago Manual of Style (16th Edition):
Nugroho, Agung Tjahjo. “Microwave tomography.” 2016. Doctoral Dissertation, University of Manchester. Accessed March 01, 2021.
https://www.research.manchester.ac.uk/portal/en/theses/microwave-tomography(1000bea8-f286-42dc-9def-8aa09411160e).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.677742.
MLA Handbook (7th Edition):
Nugroho, Agung Tjahjo. “Microwave tomography.” 2016. Web. 01 Mar 2021.
Vancouver:
Nugroho AT. Microwave tomography. [Internet] [Doctoral dissertation]. University of Manchester; 2016. [cited 2021 Mar 01].
Available from: https://www.research.manchester.ac.uk/portal/en/theses/microwave-tomography(1000bea8-f286-42dc-9def-8aa09411160e).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.677742.
Council of Science Editors:
Nugroho AT. Microwave tomography. [Doctoral Dissertation]. University of Manchester; 2016. Available from: https://www.research.manchester.ac.uk/portal/en/theses/microwave-tomography(1000bea8-f286-42dc-9def-8aa09411160e).html ; http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.677742
University of Manchester
9.
Nugroho, Agung Tjahjo.
Microwave Tomography.
Degree: 2015, University of Manchester
URL: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:278719
► This thesis reports on the research carried out in the area of Microwave Tomography (MWT) where the study aims to develop inversion algorithms to obtain…
(more)
▼ This thesis reports on the research carried out in
the area of Microwave Tomography (MWT) where the study aims to
develop inversion algorithms to obtain cheap and stable solutions
of MWT
inverse scattering
problems which are mathematically
formulated as nonlinear ill posed
problems. The study develops two
algorithms namely Inexact Newton Backtracking Method (INBM) and
Newton Iterative-Conjugate Gradient on Normal Equation (NI-CGNE)
which are based on Newton method. These algorithms apply implicit
solutions of the Newton equations with unspecific manner
functioning as the regularized step size of the Newton iterative.
The two developed methods were tested by the use of numerical
examples and experimental data gained by the MWT system of the
University of Manchester. The numerical experiments were done on
samples with dielectric contrast objects containing different kinds
of materials and lossy materials. Meanwhile, the quality of the
methods is evaluated by comparingthem with the Levenberg Marquardt
method (LM). Under the natural assumption that the INBM is a
regularized method and the CGNE is a semi regularized method, the
results of experiments show that INBM and NI-CGNE improve the
speed, the spatial resolutions and the quality of direct
regularization method by means of the LM method. The experiments
also show that the developed algorithms are more flexible to
theeffect of noise and lossy materials compared with the LM
algorithm..
Advisors/Committee Members: Wu, Zhipeng.
Subjects/Keywords: Microwave Tomography; Inverse Problems
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APA (6th Edition):
Nugroho, A. T. (2015). Microwave Tomography. (Doctoral Dissertation). University of Manchester. Retrieved from http://www.manchester.ac.uk/escholar/uk-ac-man-scw:278719
Chicago Manual of Style (16th Edition):
Nugroho, Agung Tjahjo. “Microwave Tomography.” 2015. Doctoral Dissertation, University of Manchester. Accessed March 01, 2021.
http://www.manchester.ac.uk/escholar/uk-ac-man-scw:278719.
MLA Handbook (7th Edition):
Nugroho, Agung Tjahjo. “Microwave Tomography.” 2015. Web. 01 Mar 2021.
Vancouver:
Nugroho AT. Microwave Tomography. [Internet] [Doctoral dissertation]. University of Manchester; 2015. [cited 2021 Mar 01].
Available from: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:278719.
Council of Science Editors:
Nugroho AT. Microwave Tomography. [Doctoral Dissertation]. University of Manchester; 2015. Available from: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:278719
University of Texas – Austin
10.
Goswami, Pulak.
Recovering the payoff structure of a utility maximizing agent.
Degree: PhD, Mathematics, 2016, University of Texas – Austin
URL: http://hdl.handle.net/2152/40299
► Any agent with access to information that is not available to the market at large is considered an ‘insider’. It is possible to interpret the…
(more)
▼ Any agent with access to information that is not available to the market at large is considered an ‘insider’. It is possible to interpret the effect of this private information as change in the insider’s probability measure. In the case of exponential utility, logarithm of the Radon-Nikodym derivative for the change in measure will appear as a random endowment in the objective the insider would maximize with respect to the original measure. The goal of this paper is to find conditions under which it is possible to recover the structure of this random endowment given only a single trajectory of his/her wealth. To do this, it is assumed that the random endowment is a function of the terminal value of the state variable and that the market is complete.
Advisors/Committee Members: Žitković, Gordan (advisor), Sirbu, Mihai (committee member), Pavlovic, Natasa (committee member), Larsen, Kasper (committee member).
Subjects/Keywords: Inverse problems; Insider trading
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Chicago ·
MLA ·
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APA (6th Edition):
Goswami, P. (2016). Recovering the payoff structure of a utility maximizing agent. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/40299
Chicago Manual of Style (16th Edition):
Goswami, Pulak. “Recovering the payoff structure of a utility maximizing agent.” 2016. Doctoral Dissertation, University of Texas – Austin. Accessed March 01, 2021.
http://hdl.handle.net/2152/40299.
MLA Handbook (7th Edition):
Goswami, Pulak. “Recovering the payoff structure of a utility maximizing agent.” 2016. Web. 01 Mar 2021.
Vancouver:
Goswami P. Recovering the payoff structure of a utility maximizing agent. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2016. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/2152/40299.
Council of Science Editors:
Goswami P. Recovering the payoff structure of a utility maximizing agent. [Doctoral Dissertation]. University of Texas – Austin; 2016. Available from: http://hdl.handle.net/2152/40299
Vanderbilt University
11.
Villalobos Guillén, Cristóbal.
A Measure Theoretic Approach for the Recovery of Remanent Magnetizations.
Degree: PhD, Mathematics, 2019, Vanderbilt University
URL: http://hdl.handle.net/1803/11475
► This work is motivated by the problem of recovering the magnetization M of a rock sample from a given set of measurements for the magnetic…
(more)
▼ This work is motivated by the problem of recovering the magnetization M of a rock sample from
a given set of measurements for the magnetic field it generates. Modeling the magnetization by an
R 3 -valued measure, we focus on the study of
inverse problems for the Poisson equation with source
term the divergence of M; that is,
∆Φ = divM,
where Φ denotes the Magnetic Scalar Potential whose gradient is assumed to be known on a set
disjoint from the support of the measure M. We develop methods for recovering M based on total
variation regularization of measures. We provide sufficient conditions for the unique recovery of a
magnetization in cases where it is uni-directional or when the magnetization has a support which
is sparse in the sense that it is purely 1-unrectifiable.
In the last chapter we work on the ideal case where the magnetized sample is contained in a
subset of the horizontal plane. For this case we show that all magnetizations which do not generate
a magnetic field can be decomposed as a superposition of loops. The findings presented in this
chapter rely on the theory of functions of Bounded Variation and sets of finite perimeter and give
a characterization for magnetizations that do not generate a magnetic field.
Numerical examples are provided to illustrate the main theoretical results.
Advisors/Committee Members: Marcelo M. Disconzi (committee member), Guilherme A.R. Gualda (committee member), Edward B. Saff (committee member), Akram Aldroubi (committee member), Douglas P. Hardin (Committee Chair).
Subjects/Keywords: geometric measure theory; BV fucntions; Inverse problems; Inverse problems in electromagnetism
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Chicago ·
MLA ·
Vancouver ·
CSE |
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APA (6th Edition):
Villalobos Guillén, C. (2019). A Measure Theoretic Approach for the Recovery of Remanent Magnetizations. (Doctoral Dissertation). Vanderbilt University. Retrieved from http://hdl.handle.net/1803/11475
Chicago Manual of Style (16th Edition):
Villalobos Guillén, Cristóbal. “A Measure Theoretic Approach for the Recovery of Remanent Magnetizations.” 2019. Doctoral Dissertation, Vanderbilt University. Accessed March 01, 2021.
http://hdl.handle.net/1803/11475.
MLA Handbook (7th Edition):
Villalobos Guillén, Cristóbal. “A Measure Theoretic Approach for the Recovery of Remanent Magnetizations.” 2019. Web. 01 Mar 2021.
Vancouver:
Villalobos Guillén C. A Measure Theoretic Approach for the Recovery of Remanent Magnetizations. [Internet] [Doctoral dissertation]. Vanderbilt University; 2019. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/1803/11475.
Council of Science Editors:
Villalobos Guillén C. A Measure Theoretic Approach for the Recovery of Remanent Magnetizations. [Doctoral Dissertation]. Vanderbilt University; 2019. Available from: http://hdl.handle.net/1803/11475
Victoria University of Wellington
12.
Faegh-Lashgary, Pegah.
Modelling geodetic observations of postseismic displacement in the central and southern South Island of New Zealand.
Degree: 2016, Victoria University of Wellington
URL: http://hdl.handle.net/10063/5563
► The last seven years have seen southern New Zealand a ected by several large and damaging earthquakes: the moment magnitude (MW) 7.8 Dusky Sound earthquake…
(more)
▼ The last seven years have seen southern New Zealand a ected by several large and damaging earthquakes: the moment magnitude (MW) 7.8 Dusky Sound earthquake on 15 July 2009, the MW 7.1 Dar eld (Canterbury) earthquake on 4 September 2010, and most notably the MW 6.2 Christchurch earthquake on 22 February 2011 and the protracted aftershock sequence. In this thesis, we address the postseismic displacement produced by these earthquakes using methods of satellite-based geodetic measurement, known as Interferometric Synthetic Aperture Radar (InSAR) and Global Positioning System (GPS), and computational modelling.
We observe several ground displacement features in the Canterbury and Fiordland regions during three periods: 1) Following the Dusky Sound earthquake; 2) Following the Dar eld earthquake and prior to the Christchurch earthquake; and 3) Following the Christchurch earthquake until February 2015.
The ground displacement associated with postseismic motion following the Dusky Sound earthquake has been measured by continuous and campaign GPS data acquired in August 2009, in conjunction with Di erential Interferometric Synthetic Aperture Radar (DInSAR) observations. We use an afterslip model, estimated by temporal inversion of geodetic data, with combined viscoelastic rebound model to account for the observed spatio-temporal patterns of displacement. The two postseismic processes together induce a signi cant displacement corresponding to principal extensional and contractual strain rates of the order of 10⁻⁷ and 10⁻⁸ yr⁻¹ respectively, across most of the southern South Island.
We also analyse observed postseismic displacement following the Dusky Sound earthquake using a new inversion approach in order to describe afterslip in an elasticviscoelastic medium. We develop a mathematical framework, namely the "Iterative Decoupling of Afterslip and Viscoelastic rebound (IDAV)" method, with which to invert temporally dense and spatially sparse geodetic observations. We examine the IDAV method using both numerical and analytical simulations of Green's functions.
For the post-Dar eld time interval, postseismic signals are measured within approximately one month of the mainshock. The dataset used for the post-Dar eld displacement spans the region surrounding previously unrecognised faults that ruptured during the mainshock. Poroelastic rebound in a multi-layered half-space and dilatancy recovery at shallow depths provide a satisfactory t with the observations.
For the post-Christchurch interval, campaign GPS data acquired in February 2012 to February 2015 in four successive epochs and 66 TerraSAR-X (TSX) SAR acquisitions in descending orbits between March 2011 and May 2014 reveal approximately three years of postseismic displacement. We detect movement away from the satellite of ~ 3 mm/yr in Christchurch and a gradient of displacement of ~ 4 mm/yr across a lineament extending from the westernmost end of the Western Christchurch Fault towards the eastern end of the Greendale East Fault. The postseismic signals following the…
Advisors/Committee Members: Townend, John, Williams, Charles, Hamling, Ian.
Subjects/Keywords: Satellite geodesy; Postseismic modelling; Inverse problems
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APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Faegh-Lashgary, P. (2016). Modelling geodetic observations of postseismic displacement in the central and southern South Island of New Zealand. (Doctoral Dissertation). Victoria University of Wellington. Retrieved from http://hdl.handle.net/10063/5563
Chicago Manual of Style (16th Edition):
Faegh-Lashgary, Pegah. “Modelling geodetic observations of postseismic displacement in the central and southern South Island of New Zealand.” 2016. Doctoral Dissertation, Victoria University of Wellington. Accessed March 01, 2021.
http://hdl.handle.net/10063/5563.
MLA Handbook (7th Edition):
Faegh-Lashgary, Pegah. “Modelling geodetic observations of postseismic displacement in the central and southern South Island of New Zealand.” 2016. Web. 01 Mar 2021.
Vancouver:
Faegh-Lashgary P. Modelling geodetic observations of postseismic displacement in the central and southern South Island of New Zealand. [Internet] [Doctoral dissertation]. Victoria University of Wellington; 2016. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/10063/5563.
Council of Science Editors:
Faegh-Lashgary P. Modelling geodetic observations of postseismic displacement in the central and southern South Island of New Zealand. [Doctoral Dissertation]. Victoria University of Wellington; 2016. Available from: http://hdl.handle.net/10063/5563
University of Edinburgh
13.
Zhang, Xin.
Bayesian inference in seismic tomography.
Degree: PhD, 2020, University of Edinburgh
URL: http://hdl.handle.net/1842/37012
► In a variety of scientific applications we require methods to construct three dimensional maps of properties of the interior of solid media, and in the…
(more)
▼ In a variety of scientific applications we require methods to construct three dimensional maps of properties of the interior of solid media, and in the geosciences the medium is usually the Earth's subsurface. For each such map we need the corresponding map of uncertainties in those properties in order to assess their reliability. Seismic tomography is such a method which has been used widely to study properties of the subsurface of the Earth, for example, using surface wave dispersion data. Surface wave tomography is usually conducted using a two-step method by first estimating two-dimensional (2D) surface wave phase or group velocity maps at a series of frequencies and then inverting those for the 3D spatial velocity structure through a set of 1D inversions for structure with depth beneath each geographical location. Since surface wave tomography is a highly non-linear problem, it is usually solved using Monte Carlo (MC) sampling methods. However, since the 1D inversions in the second step are usually performed independently, lateral spatial correlations of the Earth can be lost. We therefore introduce a one-step MC method which inverts for a 3D velocity structure directly from frequency-dependent surface wave travel time measurements by using a fully 3D parametrization. The method was first applied to a synthetic test and compared with two-step linearised and two-step MC methods. The results show that by including lateral spatial correlations in the inversion the new method estimates velocity models and associated uncertainty significantly better in the sense that it produces more intuitively reasonable and interpretable results, and the computation cost is also comparable to the two-step MC method. We apply the 3D MC surface wave tomography method to a real dataset recorded using a dense passive seismic array installed on the North Sea seabed. The ambient noise data of each receiver pair are cross correlated to extract Scholte waves, in which two Scholte wave modes are observed. We separated the two modes using a dispersion compensation method. For each separated mode phase velocity maps are determined using Eikonal tomography. Those phase velocity maps are then used to estimate 3D shear velocities of the subsurface. To further understand the limitation of the approach, we conducted three different inversions: the usual 1D depth inversions, a 2D inversion along a 2D cross section and a fully 3D inversion. With each inversion the shear velocity structure is extracted along the same cross section and compared. The results confirm that 1D inversions can produce errors due to independence of those inversions, whereas 2D and 3D methods improve the results by including lateral spatial correlations in the inversion. The 3D results better match an existing shear velocity model obtained from active source seismic reflection tomography. This is probably because the 3D method uses frequency-dependent measurements directly, which naturally avoids errors introduced in the first 2D Eikonal tomography step. The results show a…
Subjects/Keywords: seismic tomography; Bayesian inverse problems; ambient noise
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APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Zhang, X. (2020). Bayesian inference in seismic tomography. (Doctoral Dissertation). University of Edinburgh. Retrieved from http://hdl.handle.net/1842/37012
Chicago Manual of Style (16th Edition):
Zhang, Xin. “Bayesian inference in seismic tomography.” 2020. Doctoral Dissertation, University of Edinburgh. Accessed March 01, 2021.
http://hdl.handle.net/1842/37012.
MLA Handbook (7th Edition):
Zhang, Xin. “Bayesian inference in seismic tomography.” 2020. Web. 01 Mar 2021.
Vancouver:
Zhang X. Bayesian inference in seismic tomography. [Internet] [Doctoral dissertation]. University of Edinburgh; 2020. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/1842/37012.
Council of Science Editors:
Zhang X. Bayesian inference in seismic tomography. [Doctoral Dissertation]. University of Edinburgh; 2020. Available from: http://hdl.handle.net/1842/37012
University of Edinburgh
14.
Zhang, Xin.
Bayesian inference in seismic tomography.
Degree: PhD, 2020, University of Edinburgh
URL: https://doi.org/10.7488/era/313
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.806108
► In a variety of scientific applications we require methods to construct three dimensional maps of properties of the interior of solid media, and in the…
(more)
▼ In a variety of scientific applications we require methods to construct three dimensional maps of properties of the interior of solid media, and in the geosciences the medium is usually the Earth's subsurface. For each such map we need the corresponding map of uncertainties in those properties in order to assess their reliability. Seismic tomography is such a method which has been used widely to study properties of the subsurface of the Earth, for example, using surface wave dispersion data. Surface wave tomography is usually conducted using a two-step method by first estimating two-dimensional (2D) surface wave phase or group velocity maps at a series of frequencies and then inverting those for the 3D spatial velocity structure through a set of 1D inversions for structure with depth beneath each geographical location. Since surface wave tomography is a highly non-linear problem, it is usually solved using Monte Carlo (MC) sampling methods. However, since the 1D inversions in the second step are usually performed independently, lateral spatial correlations of the Earth can be lost. We therefore introduce a one-step MC method which inverts for a 3D velocity structure directly from frequency-dependent surface wave travel time measurements by using a fully 3D parametrization. The method was first applied to a synthetic test and compared with two-step linearised and two-step MC methods. The results show that by including lateral spatial correlations in the inversion the new method estimates velocity models and associated uncertainty significantly better in the sense that it produces more intuitively reasonable and interpretable results, and the computation cost is also comparable to the two-step MC method. We apply the 3D MC surface wave tomography method to a real dataset recorded using a dense passive seismic array installed on the North Sea seabed. The ambient noise data of each receiver pair are cross correlated to extract Scholte waves, in which two Scholte wave modes are observed. We separated the two modes using a dispersion compensation method. For each separated mode phase velocity maps are determined using Eikonal tomography. Those phase velocity maps are then used to estimate 3D shear velocities of the subsurface. To further understand the limitation of the approach, we conducted three different inversions: the usual 1D depth inversions, a 2D inversion along a 2D cross section and a fully 3D inversion. With each inversion the shear velocity structure is extracted along the same cross section and compared. The results confirm that 1D inversions can produce errors due to independence of those inversions, whereas 2D and 3D methods improve the results by including lateral spatial correlations in the inversion. The 3D results better match an existing shear velocity model obtained from active source seismic reflection tomography. This is probably because the 3D method uses frequency-dependent measurements directly, which naturally avoids errors introduced in the first 2D Eikonal tomography step. The results show a…
Subjects/Keywords: seismic tomography; Bayesian inverse problems; ambient noise
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APA ·
Chicago ·
MLA ·
Vancouver ·
CSE |
Export
to Zotero / EndNote / Reference
Manager
APA (6th Edition):
Zhang, X. (2020). Bayesian inference in seismic tomography. (Doctoral Dissertation). University of Edinburgh. Retrieved from https://doi.org/10.7488/era/313 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.806108
Chicago Manual of Style (16th Edition):
Zhang, Xin. “Bayesian inference in seismic tomography.” 2020. Doctoral Dissertation, University of Edinburgh. Accessed March 01, 2021.
https://doi.org/10.7488/era/313 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.806108.
MLA Handbook (7th Edition):
Zhang, Xin. “Bayesian inference in seismic tomography.” 2020. Web. 01 Mar 2021.
Vancouver:
Zhang X. Bayesian inference in seismic tomography. [Internet] [Doctoral dissertation]. University of Edinburgh; 2020. [cited 2021 Mar 01].
Available from: https://doi.org/10.7488/era/313 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.806108.
Council of Science Editors:
Zhang X. Bayesian inference in seismic tomography. [Doctoral Dissertation]. University of Edinburgh; 2020. Available from: https://doi.org/10.7488/era/313 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.806108
Virginia Tech
15.
Hebbur Venkata Subba Rao, Vishwas.
Adjoint based solution and uncertainty quantification techniques for variational inverse problems.
Degree: PhD, Computer Science and Applications, 2015, Virginia Tech
URL: http://hdl.handle.net/10919/76665
► Variational inverse problems integrate computational simulations of physical phenomena with physical measurements in an informational feedback control system. Control parameters of the computational model are…
(more)
▼ Variational
inverse problems integrate computational simulations of physical phenomena with physical measurements in an informational feedback control system. Control parameters of the computational model are optimized such that the simulation results fit the physical measurements.The solution procedure is computationally expensive since it involves running the simulation computer model (the emph{forward model}) and the associated emph {adjoint model} multiple times. In practice, our knowledge of the underlying physics is incomplete and hence the associated computer model is laden with emph {model errors}. Similarly, it is not possible to measure the physical quantities exactly and hence the measurements are associated with emph {data errors}. The errors in data and model adversely affect the inference solutions. This work develops methods to address the challenges posed by the computational costs and by the impact of data and model errors in solving variational
inverse problems.
Variational
inverse problems of interest here are formulated as optimization
problems constrained by partial differential equations (PDEs). The solution process requires multiple evaluations of the constraints, therefore multiple solutions of the associated PDE. To alleviate the computational costs we develop a parallel in time discretization algorithm based on a nonlinear optimization approach. Like in the emph{parareal} approach, the time interval is partitioned into subintervals, and local time integrations are carried out in parallel. Solution continuity equations across interval boundaries are added as constraints. All the computational steps - forward solutions, gradients, and Hessian-vector products - involve only ideally parallel computations and therefore are highly scalable.
This work develops a systematic mathematical framework to compute the impact of data and model errors on the solution to the variational
inverse problems. The computational algorithm makes use of first and second order adjoints and provides an a-posteriori error estimate for a quantity of interest defined on the
inverse solution (i.e., an aspect of the
inverse solution). We illustrate the estimation algorithm on a shallow water model and on the Weather Research and Forecast model.
Presence of outliers in measurement data is common, and this negatively impacts the solution to variational
inverse problems. The traditional approach, where the
inverse problem is formulated as a minimization problem in L
2 norm, is especially sensitive to large data errors. To alleviate the impact of data outliers we propose to use robust norms such as the L
1 and Huber norm in data assimilation. This work develops a systematic mathematical framework to perform three and four dimensional variational data assimilation using L
1 and Huber norms. The power of this approach is demonstrated by solving data assimilation
problems where measurements contain outliers.
Advisors/Committee Members: Sandu, Adrian (committeechair), Ribbens, Calvin J. (committee member), Constantinescu, Emil Mihai (committee member), De Sturler, Eric (committee member), Cao, Yang (committee member).
Subjects/Keywords: Data assimilation; Inverse problems; sensitivity analysis
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APA ·
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MLA ·
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APA (6th Edition):
Hebbur Venkata Subba Rao, V. (2015). Adjoint based solution and uncertainty quantification techniques for variational inverse problems. (Doctoral Dissertation). Virginia Tech. Retrieved from http://hdl.handle.net/10919/76665
Chicago Manual of Style (16th Edition):
Hebbur Venkata Subba Rao, Vishwas. “Adjoint based solution and uncertainty quantification techniques for variational inverse problems.” 2015. Doctoral Dissertation, Virginia Tech. Accessed March 01, 2021.
http://hdl.handle.net/10919/76665.
MLA Handbook (7th Edition):
Hebbur Venkata Subba Rao, Vishwas. “Adjoint based solution and uncertainty quantification techniques for variational inverse problems.” 2015. Web. 01 Mar 2021.
Vancouver:
Hebbur Venkata Subba Rao V. Adjoint based solution and uncertainty quantification techniques for variational inverse problems. [Internet] [Doctoral dissertation]. Virginia Tech; 2015. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/10919/76665.
Council of Science Editors:
Hebbur Venkata Subba Rao V. Adjoint based solution and uncertainty quantification techniques for variational inverse problems. [Doctoral Dissertation]. Virginia Tech; 2015. Available from: http://hdl.handle.net/10919/76665
Georgia State University
16.
Akossi, Aurelie.
COMPARISON OF VARIOUS DISCRETIZATION ALGORITHMS FOR STABLE ESTIMATION OF DISEASE PARAMETERS AND FORECASTING IN EPIDEMIOLOGY.
Degree: PhD, Mathematics and Statistics, 2019, Georgia State University
URL: https://scholarworks.gsu.edu/math_diss/62
► Stable estimation of system parameters for infectious disease outbreaks is of paramount importance to the design of adequate forecasting algorithms. Oftentimes parameter estimation procedures…
(more)
▼ Stable estimation of system parameters for infectious disease outbreaks is of paramount importance to the design of adequate forecasting algorithms. Oftentimes parameter estimation procedures are cast as ODE-constrained nonlinear least squares
problems, where infinite dimensional time dependent disease parameters need to be recovered from finite dimensional data sets. As the result, the Jacobian of the corresponding parameter-to-data operator is generally illconditioned and may be numerically singular. When such an operator is fitted to noise-contaminated epidemiological data, the estimated parameters tend to be entirely unreliable due to severe error propagation into the approximate solution. The sources of noise in the reported incidence data vary for different types of diseases and can be attributed to possible under or over reporting owing to, for instance, a large proportion of asymptomatic cases or false diagnostics. In our study we use the Levenberg-Marquardt algorithm to reconstruct a variable transmission rate. The regularization provided by this optimization scheme, which is a penalized version of the Gauss-Newton procedure, is enforced by the appropriate problem-oriented discretization tools. Specifically, we compare what we call parametric and non-parametric discretization routines. By parametric discretization we mean that the transmission rate is modeled by a pre-defined expression that involves only few parameters such as, for example, a declining transmission rate defined by a hyperbolic, harmonic, or exponential function. In a nonparametric discretization scheme the transmission rate is projected onto a subspace spanned by a finite set of orthogonal polynomials, or spline functions. Depending on the nature of the transmission, one may use Legendre or Chebyshev polynomials, B-splines, wavelets, or other base elements. The main goal of our project is to see how parametric and non-parametric discretization schemes compare in terms of accuracy of parameter estimation and in terms of their ability to provide a reliable forecasting tool. Numerical experiments with both synthetic and real data will be presented.
Advisors/Committee Members: Alexandra Smirnova, Gerardo Chowell.
Subjects/Keywords: Inverse Problems; Epidemiology; Regularization; Parameter Estimation; Forecasting
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APA ·
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MLA ·
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Export
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APA (6th Edition):
Akossi, A. (2019). COMPARISON OF VARIOUS DISCRETIZATION ALGORITHMS FOR STABLE ESTIMATION OF DISEASE PARAMETERS AND FORECASTING IN EPIDEMIOLOGY. (Doctoral Dissertation). Georgia State University. Retrieved from https://scholarworks.gsu.edu/math_diss/62
Chicago Manual of Style (16th Edition):
Akossi, Aurelie. “COMPARISON OF VARIOUS DISCRETIZATION ALGORITHMS FOR STABLE ESTIMATION OF DISEASE PARAMETERS AND FORECASTING IN EPIDEMIOLOGY.” 2019. Doctoral Dissertation, Georgia State University. Accessed March 01, 2021.
https://scholarworks.gsu.edu/math_diss/62.
MLA Handbook (7th Edition):
Akossi, Aurelie. “COMPARISON OF VARIOUS DISCRETIZATION ALGORITHMS FOR STABLE ESTIMATION OF DISEASE PARAMETERS AND FORECASTING IN EPIDEMIOLOGY.” 2019. Web. 01 Mar 2021.
Vancouver:
Akossi A. COMPARISON OF VARIOUS DISCRETIZATION ALGORITHMS FOR STABLE ESTIMATION OF DISEASE PARAMETERS AND FORECASTING IN EPIDEMIOLOGY. [Internet] [Doctoral dissertation]. Georgia State University; 2019. [cited 2021 Mar 01].
Available from: https://scholarworks.gsu.edu/math_diss/62.
Council of Science Editors:
Akossi A. COMPARISON OF VARIOUS DISCRETIZATION ALGORITHMS FOR STABLE ESTIMATION OF DISEASE PARAMETERS AND FORECASTING IN EPIDEMIOLOGY. [Doctoral Dissertation]. Georgia State University; 2019. Available from: https://scholarworks.gsu.edu/math_diss/62
17.
DeCamp, Linda.
Regularized Numerical Algorithms For Stable Parameter Estimation In Epidemiology And Implications For Forecasting.
Degree: PhD, Mathematics and Statistics, 2017, Georgia State University
URL: https://scholarworks.gsu.edu/math_diss/45
► When an emerging outbreak occurs, stable parameter estimation and reliable projections of future incidence cases using limited (early) data can play an important role…
(more)
▼ When an emerging outbreak occurs, stable parameter estimation and reliable projections of future incidence cases using limited (early) data can play an important role in optimal allocation of resources and in the development of effective public health intervention programs. However, the
inverse parameter identification problem is ill-posed and cannot be solved with classical tools of computational mathematics. In this dissertation, various regularization methods are employed to incorporate stability in parameter estimation algorithms. The recovered parameters are then used to generate future incident curves as well as the carrying capacity of the epidemic and the turning point of the outbreak.
For the nonlinear generalized Richards model of disease progression, we develop a novel iteratively regularized Gauss-Newton-type algorithm to reconstruct major characteristics of an emerging infection. This problem-oriented numerical scheme takes full advantage of a priori information available for our specific application in order to stabilize the iterative process. Another important aspect of our research is a reliable estimation of time-dependent transmission rate in a compartmental SEIR disease model. To that end, the ODE-constrained minimization problem is reduced to a linear Volterra integral equation of the first kind, and a combination of regularizing filters is employed to approximate the unknown transmission parameter in a stable manner. To justify our theoretical findings, extensive numerical experiments have been conducted with both synthetic and real data for various infectious diseases.
Advisors/Committee Members: Alexandra Smirnova, Vladimir Bondarenko, Gerardo Chowell-Puente, Michael Stewart.
Subjects/Keywords: Inverse Problems; Epidemiology; Regularization; Parameter Estimation; Forecasting
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APA (6th Edition):
DeCamp, L. (2017). Regularized Numerical Algorithms For Stable Parameter Estimation In Epidemiology And Implications For Forecasting. (Doctoral Dissertation). Georgia State University. Retrieved from https://scholarworks.gsu.edu/math_diss/45
Chicago Manual of Style (16th Edition):
DeCamp, Linda. “Regularized Numerical Algorithms For Stable Parameter Estimation In Epidemiology And Implications For Forecasting.” 2017. Doctoral Dissertation, Georgia State University. Accessed March 01, 2021.
https://scholarworks.gsu.edu/math_diss/45.
MLA Handbook (7th Edition):
DeCamp, Linda. “Regularized Numerical Algorithms For Stable Parameter Estimation In Epidemiology And Implications For Forecasting.” 2017. Web. 01 Mar 2021.
Vancouver:
DeCamp L. Regularized Numerical Algorithms For Stable Parameter Estimation In Epidemiology And Implications For Forecasting. [Internet] [Doctoral dissertation]. Georgia State University; 2017. [cited 2021 Mar 01].
Available from: https://scholarworks.gsu.edu/math_diss/45.
Council of Science Editors:
DeCamp L. Regularized Numerical Algorithms For Stable Parameter Estimation In Epidemiology And Implications For Forecasting. [Doctoral Dissertation]. Georgia State University; 2017. Available from: https://scholarworks.gsu.edu/math_diss/45
University of Texas – Austin
18.
Gilbert, Andrew James.
Noninvasive material discrimination using spectral radiography and an inverse problem approach.
Degree: PhD, Mechanical Engineering, 2014, University of Texas – Austin
URL: http://hdl.handle.net/2152/46534
► Noninvasive material discrimination of an arbitrary object is applicable to a wide range of fields, including medical scans, security inspections, nuclear safeguards, and nuclear material…
(more)
▼ Noninvasive material discrimination of an arbitrary object is applicable to a wide range of fields, including medical scans, security inspections, nuclear safeguards, and nuclear material accountancy. In this work, we present an algorithmic framework to accurately determine material compositions from multi-spectral X-ray and neutron radiography. The algorithm uses an
inverse problem approach and regularization, which amounts to adding information to the problem; stabilizing the solution so that accurate material estimations can be made from a problem that would otherwise be intractable. First, we show the utility of the algorithm with simulated inspections of small objects, such as baggage, for small quantities of high-atomic-numbered materials (i.e. plutonium). The algorithm shows excellent sensitivity to shielded plutonium in a scan using an X-ray detector that can bin X-rays by energy. We present here a method to adaptively weight the regularization term, obtaining an optimal solution with minimal user input. Second, we explore material discrimination with high-energy, multiple-energy X-ray. Experimental X-ray data is obtained here and accurate discrimination of steel among lower-atomic-numbered materials is shown. Accurate modeling of the inspection system physics is found to be essential for accurate material estimations with this data, especially the detector response and the scattered flux on the image plane. Third, we explore the use of neutron radiography as complementary to X-ray radiography for the inspection of nuclear material storage containers. Utility of this extra data is shown, especially in detecting a hypothetical attempt to divert material. We present a method to choose inspection system design parameters (i.e. source energy and detector thickness) a priori by using the Cramér-Rao lower bound as a measure of resulting material estimation accuracy. Finally, we present methodology to use tomography data obtained with an energy discriminating detector for direct reconstruction of material attenuation coefficients.
Advisors/Committee Members: Deinert, Mark (advisor), McDonald, Benjamin (committee member), Biegalski, Steven (committee member), Ghattas, Omar (committee member), Schneider, Erich (committee member).
Subjects/Keywords: X-ray; Radiography; Inverse problems; Material discrimination
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APA (6th Edition):
Gilbert, A. J. (2014). Noninvasive material discrimination using spectral radiography and an inverse problem approach. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/46534
Chicago Manual of Style (16th Edition):
Gilbert, Andrew James. “Noninvasive material discrimination using spectral radiography and an inverse problem approach.” 2014. Doctoral Dissertation, University of Texas – Austin. Accessed March 01, 2021.
http://hdl.handle.net/2152/46534.
MLA Handbook (7th Edition):
Gilbert, Andrew James. “Noninvasive material discrimination using spectral radiography and an inverse problem approach.” 2014. Web. 01 Mar 2021.
Vancouver:
Gilbert AJ. Noninvasive material discrimination using spectral radiography and an inverse problem approach. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2014. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/2152/46534.
Council of Science Editors:
Gilbert AJ. Noninvasive material discrimination using spectral radiography and an inverse problem approach. [Doctoral Dissertation]. University of Texas – Austin; 2014. Available from: http://hdl.handle.net/2152/46534
University of Pennsylvania
19.
Levinson, Howard.
A Novel Iterative Algorithm for Solving Nonlinear Inverse Scattering Problems.
Degree: 2016, University of Pennsylvania
URL: https://repository.upenn.edu/edissertations/1843
► We introduce a novel iterative method for solving nonlinear inverse scattering problems. Inspired by the theory of nonlocality, we formulate the inverse scattering problem in…
(more)
▼ We introduce a novel iterative method for solving nonlinear inverse scattering problems. Inspired by the theory of nonlocality, we formulate the inverse scattering problem in terms of reconstructing the nonlocal unknown scattering potential V from scattered field measurements made outside a sample. Utilizing the one-to-one correspondence between V and T, the T-matrix, we iteratively search for a diagonally dominated scattering potential V corresponding to a data compatible T-matrix T. This formulation only explicitly uses the data measurements when initializing the iterations, and the size of the data set is not a limiting factor. After introducing this method, named data-compatible T-matrix completion (DCTMC), we detail numerous improvements the speed up convergence. Numerical simulations are conducted that provide evidence that DCTMC is a viable method for solving strongly nonlinear ill-posed inverse problems
with large data sets. These simulations model both scalar wave diffraction and diffuse optical tomography in three dimensions. Finally, numerical comparisons with the commonly used nonlinear iterative methods Gauss-Newton and Levenburg-Marquardt are provided.
Subjects/Keywords: Inverse Problems; Nonlinear Iterations; Scattering; Applied Mathematics
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APA (6th Edition):
Levinson, H. (2016). A Novel Iterative Algorithm for Solving Nonlinear Inverse Scattering Problems. (Thesis). University of Pennsylvania. Retrieved from https://repository.upenn.edu/edissertations/1843
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Levinson, Howard. “A Novel Iterative Algorithm for Solving Nonlinear Inverse Scattering Problems.” 2016. Thesis, University of Pennsylvania. Accessed March 01, 2021.
https://repository.upenn.edu/edissertations/1843.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Levinson, Howard. “A Novel Iterative Algorithm for Solving Nonlinear Inverse Scattering Problems.” 2016. Web. 01 Mar 2021.
Vancouver:
Levinson H. A Novel Iterative Algorithm for Solving Nonlinear Inverse Scattering Problems. [Internet] [Thesis]. University of Pennsylvania; 2016. [cited 2021 Mar 01].
Available from: https://repository.upenn.edu/edissertations/1843.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Levinson H. A Novel Iterative Algorithm for Solving Nonlinear Inverse Scattering Problems. [Thesis]. University of Pennsylvania; 2016. Available from: https://repository.upenn.edu/edissertations/1843
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Drexel University
20.
Karlovitz, Alexander.
Numerical Methods for Inversion of the One-Dimensional Diffusion Equation.
Degree: 2017, Drexel University
URL: http://hdl.handle.net/1860/idea:7407
► The one-dimensional diffusion equation comes up in a variety of physical circumstances. Both analytical and numerical methods are well understood for the forward problem. However,…
(more)
▼ The one-dimensional diffusion equation comes up in a variety of physical circumstances. Both analytical and numerical methods are well understood for the forward problem. However, methods for the inversion of this equation remain of interest in the mathematical community. In this paper, two novel inversion methods are presented, along with preliminary results from testing. The first method involves heavy use of the Lanczos Method, an algorithm which converts a basis into an orthonormal basis with some other useful properties. The second involves a direct linearization of the equation before numerical inversion.
M.S., Mathematics – Drexel University, 2017
Advisors/Committee Members: Moskow, Shari, College of Arts and Sciences.
Subjects/Keywords: Mathematics; Heat equation; Inverse problems (Differential equations)
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APA (6th Edition):
Karlovitz, A. (2017). Numerical Methods for Inversion of the One-Dimensional Diffusion Equation. (Thesis). Drexel University. Retrieved from http://hdl.handle.net/1860/idea:7407
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Karlovitz, Alexander. “Numerical Methods for Inversion of the One-Dimensional Diffusion Equation.” 2017. Thesis, Drexel University. Accessed March 01, 2021.
http://hdl.handle.net/1860/idea:7407.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Karlovitz, Alexander. “Numerical Methods for Inversion of the One-Dimensional Diffusion Equation.” 2017. Web. 01 Mar 2021.
Vancouver:
Karlovitz A. Numerical Methods for Inversion of the One-Dimensional Diffusion Equation. [Internet] [Thesis]. Drexel University; 2017. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/1860/idea:7407.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Karlovitz A. Numerical Methods for Inversion of the One-Dimensional Diffusion Equation. [Thesis]. Drexel University; 2017. Available from: http://hdl.handle.net/1860/idea:7407
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
University of Cambridge
21.
Tovey, Robert.
Mathematical challenges in electron microscopy.
Degree: PhD, 2020, University of Cambridge
URL: https://doi.org/10.17863/CAM.63763
;
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.821673
► Development of electron microscopes first started nearly 100 years ago and they are now a mature imaging modality with many applications and vast potential for…
(more)
▼ Development of electron microscopes first started nearly 100 years ago and they are now a mature imaging modality with many applications and vast potential for the future. The principal feature of electron microscopes is their resolution; they can be up to 1000 times more powerful than a visible light microscope and resolve even the smallest atoms. Furthermore, electron microscopes are also sensitive to many material properties due to the very rich interactions between electrons and other matter. Because of these capabilities, electron microscopy is used in applications as diverse as drug discovery, computer chip manufacture, and the development of solar cells. In parallel to this, the mathematical field of inverse problems has also evolved dramatically. Many new methods have been introduced to improve the recovery of unknown structures from indirect data, typically an ill-posed problem. In particular, sparsity promoting functionals such as the total variation and its extensions have been shown to be very powerful for recovering accurate physical quantities from very little and/or poor quality data. While sparsity-promoting reconstruction methods are powerful, they can also be slow, especially in a big-data setting. This trade-off forms an eternal cycle as new numerical tools are found and more powerful models are developed. The work presented in this thesis aims to marry the tools of inverse problems with the problems of electron microscopy: bringing state-of-the-art image processing techniques to bear on challenges specific to electron microscopy, developing new optimisation methods for these problems, and modelling new inverse problems to extend the capabilities of existing microscopes. One focus is the application of a directional total variation to overcome the limited angle problem in electron tomography, another is the proposal of a new inverse problem for the reconstruction of 3D strain tensor fields from electron microscopy diffraction data. The remaining contributions target numerical aspects of inverse problems, from new algorithms for non-convex problems to convex optimisation with adaptive meshes.
Subjects/Keywords: Mathematics; Optimisation; Inverse problems; Electron microscopy
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APA (6th Edition):
Tovey, R. (2020). Mathematical challenges in electron microscopy. (Doctoral Dissertation). University of Cambridge. Retrieved from https://doi.org/10.17863/CAM.63763 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.821673
Chicago Manual of Style (16th Edition):
Tovey, Robert. “Mathematical challenges in electron microscopy.” 2020. Doctoral Dissertation, University of Cambridge. Accessed March 01, 2021.
https://doi.org/10.17863/CAM.63763 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.821673.
MLA Handbook (7th Edition):
Tovey, Robert. “Mathematical challenges in electron microscopy.” 2020. Web. 01 Mar 2021.
Vancouver:
Tovey R. Mathematical challenges in electron microscopy. [Internet] [Doctoral dissertation]. University of Cambridge; 2020. [cited 2021 Mar 01].
Available from: https://doi.org/10.17863/CAM.63763 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.821673.
Council of Science Editors:
Tovey R. Mathematical challenges in electron microscopy. [Doctoral Dissertation]. University of Cambridge; 2020. Available from: https://doi.org/10.17863/CAM.63763 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.821673
Johannes Gutenberg Universität Mainz
22.
Schappel, Birgit.
Die Faktorisierungsmethode für die elektrische Impedanztomographie im Halbraum.
Degree: 2005, Johannes Gutenberg Universität Mainz
URL: http://ubm.opus.hbz-nrw.de/volltexte/2005/742/
► In der vorliegenden Arbeit wird die Faktorisierungsmethode zur Erkennung von Inhomogenitäten der Leitfähigkeit in der elektrischen Impedanztomographie auf unbeschränkten Gebieten - speziell der Halbebene bzw.…
(more)
▼ In der vorliegenden Arbeit wird die Faktorisierungsmethode zur
Erkennung von Inhomogenitäten der Leitfähigkeit in der elektrischen
Impedanztomographie auf unbeschränkten Gebieten - speziell der
Halbebene bzw. dem Halbraum - untersucht. Als Lösungsräume für das
direkte Problem, d.h. die Bestimmung des elektrischen Potentials zu
vorgegebener Leitfähigkeit und zu vorgegebenem Randstrom, führen wir
gewichtete Sobolev-Räume ein. In diesen wird die Existenz von schwachen
Lösungen des direkten Problems gezeigt und die Gültigkeit einer
Integraldarstellung für die Lösung der Laplace-Gleichung, die man bei homogener
Leitfähigkeit erhält, bewiesen. Mittels der Faktorisierungsmethode geben wir
eine explizite Charakterisierung von
Einschlüssen an, die gegenüber dem Hintergrund eine sprunghaft erhöhte
oder erniedrigte Leitfähigkeit haben. Damit ist
zugleich für diese Klasse von Leitfähigkeiten die eindeutige
Rekonstruierbarkeit der Einschlüsse bei Kenntnis der lokalen
Neumann-Dirichlet-Abbildung gezeigt.
Die mittels der Faktorisierungsmethode erhaltene Charakterisierung
der Einschlüsse haben wir in ein
numerisches Verfahren umgesetzt und sowohl im zwei- als auch im
dreidimensionalen Fall mit simulierten, teilweise gestörten Daten
getestet. Im Gegensatz zu anderen bekannten Rekonstruktionsverfahren
benötigt das hier vorgestellte keine Vorabinformation über Anzahl und
Form der Einschlüsse und hat als nicht-iteratives Verfahren einen
vergleichsweise geringen Rechenaufwand.
In this thesis we consider the factorization method for the reconstruction of
inhomogeneities in Electrical Impedance Tomography on unbounded
domains.
As a model for an unbounded domain with nearly planar boundary the
upper half plane and the upper half space are used.
As solution spaces for the direct problem, i.e. the determination of the
electric potential for given conductivity and given boundary
current, we introduce weighted Sobolev spaces.
In these spaces existence of weak solutions of the direct problem is
proven and an integral representation for the weak solution of the
Laplace equation, which we obtain for a homogeneous domain, is
established.
Using the factorization method we prove an explicit characterization
of inclusions where the conductivity differs significantly from the
background conductivity. This result also provides the unique
identifiability for this class of conductivities from the knowledge of
the local Neumann-to-Dirichlet operator.
The characterization of the inclusions obtained by the factorization
method is then translated into a reconstruction algorithm. The method
is tested in two dimensions as well as in three dimensions using
simulated, partially noisy data.
In contrast to other known reconstruction algorithms the method
presented in this thesis does not need any a priori knowledge about
the number and the shape of the inclusions. It is a non iterative
algorithm and such has comparatively small computational cost.
Subjects/Keywords: Inverse Probleme; inverse problems; Mathematics
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APA ·
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APA (6th Edition):
Schappel, B. (2005). Die Faktorisierungsmethode für die elektrische Impedanztomographie im Halbraum. (Doctoral Dissertation). Johannes Gutenberg Universität Mainz. Retrieved from http://ubm.opus.hbz-nrw.de/volltexte/2005/742/
Chicago Manual of Style (16th Edition):
Schappel, Birgit. “Die Faktorisierungsmethode für die elektrische Impedanztomographie im Halbraum.” 2005. Doctoral Dissertation, Johannes Gutenberg Universität Mainz. Accessed March 01, 2021.
http://ubm.opus.hbz-nrw.de/volltexte/2005/742/.
MLA Handbook (7th Edition):
Schappel, Birgit. “Die Faktorisierungsmethode für die elektrische Impedanztomographie im Halbraum.” 2005. Web. 01 Mar 2021.
Vancouver:
Schappel B. Die Faktorisierungsmethode für die elektrische Impedanztomographie im Halbraum. [Internet] [Doctoral dissertation]. Johannes Gutenberg Universität Mainz; 2005. [cited 2021 Mar 01].
Available from: http://ubm.opus.hbz-nrw.de/volltexte/2005/742/.
Council of Science Editors:
Schappel B. Die Faktorisierungsmethode für die elektrische Impedanztomographie im Halbraum. [Doctoral Dissertation]. Johannes Gutenberg Universität Mainz; 2005. Available from: http://ubm.opus.hbz-nrw.de/volltexte/2005/742/
Johannes Gutenberg Universität Mainz
23.
Gebauer, Bastian.
Gebietserkennung mit der Faktorisierungsmethode.
Degree: 2006, Johannes Gutenberg Universität Mainz
URL: http://ubm.opus.hbz-nrw.de/volltexte/2006/1137/
► In der vorliegenden Arbeit wird die Faktorisierungsmethode zur Erkennung von Gebieten mit sprunghaft abweichenden Materialparametern untersucht. Durch eine abstrakte Formulierung beweisen wir die der Methode…
(more)
▼ In der vorliegenden Arbeit wird die Faktorisierungsmethode zur Erkennung von Gebieten mit sprunghaft abweichenden Materialparametern untersucht. Durch eine abstrakte Formulierung beweisen wir die der Methode zugrunde liegende Bildraumidentität für allgemeine reelle elliptische Probleme und deduzieren bereits bekannte und neue Anwendungen der Methode.
Für das spezielle Problem, magnetische oder perfekt elektrisch leitende Objekte durch niederfrequente elektromagnetische Strahlung zu lokalisieren, zeigen wir die eindeutige Lösbarkeit des direkten Problems für hinreichend kleine Frequenzen und die Konvergenz der Lösungen gegen die der elliptischen Gleichungen der Magnetostatik. Durch Anwendung unseres allgemeinen Resultats erhalten wir die eindeutige Rekonstruierbarkeit der gesuchten Objekte aus elektromagnetischen Messungen und einen numerischen Algorithmus zur Lokalisierung der Objekte.
An einem Musterproblem untersuchen wir, wie durch parabolische Differentialgleichungen beschriebene Einschlüsse in einem durch elliptische Differentialgleichungen beschriebenen Gebiet rekonstruiert werden können. Dabei beweisen wir die eindeutige Lösbarkeit des zugrunde liegenden parabolisch-elliptischen direkten Problems und erhalten durch eine Erweiterung der Faktorisierungsmethode die eindeutige Rekonstruierbarkeit der Einschlüsse sowie einen numerischen Algorithmus zur praktischen Umsetzung der Methode.
In this work we study the Factorization Method for detecting inclusions in a domain where the material parameters of the inclusions significantly differ from that of the rest of the domain. The method is based on a range identity. Using an abstract formulation we prove that this identity holds for general real elliptic problems and deduce some known as well as new applications for the method.
For the special problem of locating magnetic or perfectly conducting objects by low-frequency electromagnetic scattering we show the unique solvability of the direct problem for small frequencies and the convergence of the solutions to that of the elliptic equations of magnetostatics. Using our general result for the Factorization Method we obtain the unique reconstructibility of the objects from electromagnetic measurements and a numerical algorithm for locating the objects.
On a sample problem we study how inclusions that are described by a parabolic differential equation can be located in a domain described by an elliptic differential equation. We prove the unique solvability of the underlying parabolic-elliptic problem and by an extension of the Factorization Method we obtain the unique reconstructibility of the inclusions and a numerical algorithm for the practical implementation of the method.
Subjects/Keywords: Inverse Probleme; inverse problems; Mathematics
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APA (6th Edition):
Gebauer, B. (2006). Gebietserkennung mit der Faktorisierungsmethode. (Doctoral Dissertation). Johannes Gutenberg Universität Mainz. Retrieved from http://ubm.opus.hbz-nrw.de/volltexte/2006/1137/
Chicago Manual of Style (16th Edition):
Gebauer, Bastian. “Gebietserkennung mit der Faktorisierungsmethode.” 2006. Doctoral Dissertation, Johannes Gutenberg Universität Mainz. Accessed March 01, 2021.
http://ubm.opus.hbz-nrw.de/volltexte/2006/1137/.
MLA Handbook (7th Edition):
Gebauer, Bastian. “Gebietserkennung mit der Faktorisierungsmethode.” 2006. Web. 01 Mar 2021.
Vancouver:
Gebauer B. Gebietserkennung mit der Faktorisierungsmethode. [Internet] [Doctoral dissertation]. Johannes Gutenberg Universität Mainz; 2006. [cited 2021 Mar 01].
Available from: http://ubm.opus.hbz-nrw.de/volltexte/2006/1137/.
Council of Science Editors:
Gebauer B. Gebietserkennung mit der Faktorisierungsmethode. [Doctoral Dissertation]. Johannes Gutenberg Universität Mainz; 2006. Available from: http://ubm.opus.hbz-nrw.de/volltexte/2006/1137/
24.
Bingham, Kenrick.
The Blagoveščenskiĭ Identity and the Inverse Scattering Problem.
Degree: 2005, Helsinki University of Technology
URL: http://lib.tkk.fi/Diss/2005/isbn9512276143/
► The inverse scattering problem for the plasma wave equation [∂2t − ∆ + q(x)] u(x,t) = 0 in three space dimensions is considered in this…
(more)
▼ The inverse scattering problem for the plasma wave equation [∂2t − ∆ + q(x)] u(x,t) = 0 in three space dimensions is considered in this thesis. It is shown that, under certain assumptions about the potential, the time domain scattering problem can be formulated equivalently in the frequency domain. Time and frequency domain techniques are combined in the subsequent analysis. The Blagoveščenskiĭ identity is generalised to the case of scattering data, assuming an inverse polynomial decay of the potential. This identity makes it possible to calculate the inner product of certain solutions of the plasma wave equation at a given time, if the corresponding incident waves and the scattering amplitude are known. In the case of a compactly supported potential, these inner products can be calculated for the time derivatives of all solutions. In the remaining part of the work, the potential is assumed to be compactly supported. A variant of the boundary control method is used to show that using appropriate superpositions of plane waves as incident waves, it is possible to excite a wave basis over a compact set. Letting this set shrink to a point, the Blagoveščenskiĭ identity provides pointwise information about the solutions. When substituted into the plasma wave equation, this yields a method for solving the inverse problem.
Annales Academiae scientiarum Fennicae. Mathematica dissertationes, ISSN 1239-6303; 142
Advisors/Committee Members: Helsinki University of Technology, Department of Engineering Physics and Mathematics, Institute of Mathematics.
Subjects/Keywords: inverse problems; inverse scattering problem; potential scattering; boundary control method
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APA (6th Edition):
Bingham, K. (2005). The Blagoveščenskiĭ Identity and the Inverse Scattering Problem. (Thesis). Helsinki University of Technology. Retrieved from http://lib.tkk.fi/Diss/2005/isbn9512276143/
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Bingham, Kenrick. “The Blagoveščenskiĭ Identity and the Inverse Scattering Problem.” 2005. Thesis, Helsinki University of Technology. Accessed March 01, 2021.
http://lib.tkk.fi/Diss/2005/isbn9512276143/.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Bingham, Kenrick. “The Blagoveščenskiĭ Identity and the Inverse Scattering Problem.” 2005. Web. 01 Mar 2021.
Vancouver:
Bingham K. The Blagoveščenskiĭ Identity and the Inverse Scattering Problem. [Internet] [Thesis]. Helsinki University of Technology; 2005. [cited 2021 Mar 01].
Available from: http://lib.tkk.fi/Diss/2005/isbn9512276143/.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Bingham K. The Blagoveščenskiĭ Identity and the Inverse Scattering Problem. [Thesis]. Helsinki University of Technology; 2005. Available from: http://lib.tkk.fi/Diss/2005/isbn9512276143/
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Colorado State University
25.
Hamilton, Sarah Jane.
Direct D-bar reconstruction algorithm for complex admittivities in W2,∞(Ω) for the 2-D EIT problem, A.
Degree: PhD, Mathematics, 2012, Colorado State University
URL: http://hdl.handle.net/10217/68173
► Electrical Impedance Tomography (EIT) is a fairly new, portable, relatively inexpensive, imaging system that requires no ionizing radiation. Electrodes are placed at the surface of…
(more)
▼ Electrical Impedance Tomography (EIT) is a fairly new, portable, relatively inexpensive, imaging system that requires no ionizing radiation. Electrodes are placed at the surface of a body and low frequency, low amplitude current is applied on the electrodes, and the resulting voltage value on each electrode is measured. By applying a basis of current patterns, one can obtain sufficient information to recover the complex admittivity distribution of the region in the plane of the electrodes. In 2000, Elisa Francini presented a nearly constructive proof that was the first approach using D-bar methods to solve the full nonlinear problem for twice-differentiable conductivities and permittivities. In this thesis the necessary formulas to turn her proof into a direct D-bar reconstruction algorithm that solves the full nonlinear admittivity problem in 2-D are described. Reconstructions for simulated Finite Element data for circular and non-circular domains are presented.
Advisors/Committee Members: Mueller, Jennifer L. (advisor), Duchateau, Paul (committee member), Tavener, Simon (committee member), Lear, Kevin (committee member).
Subjects/Keywords: Calderon problem; inverse problems; inverse conductivity problem; D-bar
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APA (6th Edition):
Hamilton, S. J. (2012). Direct D-bar reconstruction algorithm for complex admittivities in W2,∞(Ω) for the 2-D EIT problem, A. (Doctoral Dissertation). Colorado State University. Retrieved from http://hdl.handle.net/10217/68173
Chicago Manual of Style (16th Edition):
Hamilton, Sarah Jane. “Direct D-bar reconstruction algorithm for complex admittivities in W2,∞(Ω) for the 2-D EIT problem, A.” 2012. Doctoral Dissertation, Colorado State University. Accessed March 01, 2021.
http://hdl.handle.net/10217/68173.
MLA Handbook (7th Edition):
Hamilton, Sarah Jane. “Direct D-bar reconstruction algorithm for complex admittivities in W2,∞(Ω) for the 2-D EIT problem, A.” 2012. Web. 01 Mar 2021.
Vancouver:
Hamilton SJ. Direct D-bar reconstruction algorithm for complex admittivities in W2,∞(Ω) for the 2-D EIT problem, A. [Internet] [Doctoral dissertation]. Colorado State University; 2012. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/10217/68173.
Council of Science Editors:
Hamilton SJ. Direct D-bar reconstruction algorithm for complex admittivities in W2,∞(Ω) for the 2-D EIT problem, A. [Doctoral Dissertation]. Colorado State University; 2012. Available from: http://hdl.handle.net/10217/68173
26.
Szasz, Teodora.
Advanced beamforming techniques in ultrasound imaging and the associated inverse problems : Techniques avancées de formation de voies en imagerie ultrasonore et problèmes inverses associés.
Degree: Docteur es, Informatique, 2016, Université Toulouse III – Paul Sabatier
URL: http://www.theses.fr/2016TOU30221
► L'imagerie ultrasonore (US) permet de réaliser des examens médicaux non invasifs avec des méthodes d'acquisition rapides à des coûts modérés. L'imagerie cardiaque, abdominale, fœtale, ou…
(more)
▼ L'imagerie ultrasonore (US) permet de réaliser des examens médicaux non invasifs avec des méthodes d'acquisition rapides à des coûts modérés. L'imagerie cardiaque, abdominale, fœtale, ou mammaire sont quelques-unes des applications où elle est largement utilisée comme outil de diagnostic. En imagerie US classique, des ondes acoustiques sont transmises à une région d'intérêt du corps humain. Les signaux d'écho rétrodiffusés, sont ensuite formés pour créer des lignes radiofréquences. La formation de voies (FV) joue un rôle clé dans l'obtention des images US, car elle influence la résolution et le contraste de l'image finale. L'objectif de ce travail est de modéliser la formation de voies comme un problème inverse liant les données brutes aux signaux RF. Le modèle de formation de voies proposé ici améliore le contraste et la résolution spatiale des images échographiques par rapport aux techniques de FV existants. Dans un premier temps, nous nous sommes concentrés sur des méthodes de FV en imagerie US. Nous avons brièvement passé en revue les techniques de formation de voies les plus courantes, en commencent par la méthode par retard et somme standard puis en utilisant les techniques de formation de voies adaptatives. Ensuite, nous avons étudié l'utilisation de signaux qui exploitent une représentation parcimonieuse de l'image US dans le cadre de la formation de voies. Les approches proposées détectent les réflecteurs forts du milieu sur la base de critères bayésiens. Nous avons finalement développé une nouvelle façon d'aborder la formation de voies en imagerie US, en la formulant comme un problème inverse linéaire liant les échos réfléchis au signal final. L'intérêt majeur de notre approche est la flexibilité dans le choix des hypothèses statistiques sur le signal avant la formation de voies et sa robustesse dans à un nombre réduit d'émissions. Finalement, nous présentons une nouvelle méthode de formation de voies pour l'imagerie US basée sur l'utilisation de caractéristique statistique des signaux supposée alpha-stable.
Ultrasound (US) allows non-invasive and ultra-high frame rate imaging procedures at reduced costs. Cardiac, abdominal, fetal, and breast imaging are some of the applications where it is extensively used as diagnostic tool. In a classical US scanning process, short acoustic pulses are transmitted through the region-of-interest of the human body. The backscattered echo signals are then beamformed for creating radiofrequency(RF) lines. Beamforming (BF) plays a key role in US image formation, influencing the resolution and the contrast of final image. The objective of this thesis is to model BF as an inverse problem, relating the raw channel data to the signals to be recovered. The proposed BF framework improves the contrast and the spatial resolution of the US images, compared with the existing BF methods. To begin with, we investigated the existing BF methods in medical US imaging. We briefly review the most common BF techniques, starting with the standard delay-and-sum BF method and emerging to the…
Advisors/Committee Members: Basarab, Adrian (thesis director), Kouamé, Denis (thesis director).
Subjects/Keywords: Imagerie ultrasonore; Formation de voies adaptatives; Problèmes inverse; Ultrasound imaging; Adaptive beamforming; Inverse problems
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APA (6th Edition):
Szasz, T. (2016). Advanced beamforming techniques in ultrasound imaging and the associated inverse problems : Techniques avancées de formation de voies en imagerie ultrasonore et problèmes inverses associés. (Doctoral Dissertation). Université Toulouse III – Paul Sabatier. Retrieved from http://www.theses.fr/2016TOU30221
Chicago Manual of Style (16th Edition):
Szasz, Teodora. “Advanced beamforming techniques in ultrasound imaging and the associated inverse problems : Techniques avancées de formation de voies en imagerie ultrasonore et problèmes inverses associés.” 2016. Doctoral Dissertation, Université Toulouse III – Paul Sabatier. Accessed March 01, 2021.
http://www.theses.fr/2016TOU30221.
MLA Handbook (7th Edition):
Szasz, Teodora. “Advanced beamforming techniques in ultrasound imaging and the associated inverse problems : Techniques avancées de formation de voies en imagerie ultrasonore et problèmes inverses associés.” 2016. Web. 01 Mar 2021.
Vancouver:
Szasz T. Advanced beamforming techniques in ultrasound imaging and the associated inverse problems : Techniques avancées de formation de voies en imagerie ultrasonore et problèmes inverses associés. [Internet] [Doctoral dissertation]. Université Toulouse III – Paul Sabatier; 2016. [cited 2021 Mar 01].
Available from: http://www.theses.fr/2016TOU30221.
Council of Science Editors:
Szasz T. Advanced beamforming techniques in ultrasound imaging and the associated inverse problems : Techniques avancées de formation de voies en imagerie ultrasonore et problèmes inverses associés. [Doctoral Dissertation]. Université Toulouse III – Paul Sabatier; 2016. Available from: http://www.theses.fr/2016TOU30221
27.
Văcar, Cornelia Paula.
Inversion for textured images : unsupervised myopic deconvolution, model selection, deconvolution-segmentation : Inversion pour image texturée : déconvolution myope non supervisée, choix de modèles, déconvolution-segmentation.
Degree: Docteur es, Automatique, productique, signal et image, ingénierie cognitique, 2014, Bordeaux
URL: http://www.theses.fr/2014BORD0131
► Ce travail est dédié à la résolution de plusieurs problèmes de grand intérêt en traitement d’images : segmentation, choix de modèle et estimation de paramètres,…
(more)
▼ Ce travail est dédié à la résolution de plusieurs problèmes de grand intérêt en traitement d’images : segmentation, choix de modèle et estimation de paramètres, pour le cas spécifique d’images texturées indirectement observées (convoluées et bruitées). Dans ce contexte, les contributions de cette thèse portent sur trois plans différents : modéle, méthode et algorithmique.Du point de vue modélisation de la texture, un nouveaumodèle non-gaussien est proposé. Ce modèle est défini dans le domaine de Fourier et consiste en un mélange de Gaussiennes avec une Densité Spectrale de Puissance paramétrique.Du point de vueméthodologique, la contribution est triple –troisméthodes Bayésiennes pour résoudre de manière :–optimale–non-supervisée–des problèmes inverses en imagerie dans le contexte d’images texturées ndirectement observées, problèmes pas abordés dans la littérature jusqu’à présent.Plus spécifiquement,1. la première méthode réalise la déconvolution myope non-supervisée et l’estimation des paramètres de la texture,2. la deuxième méthode est dédiée à la déconvolution non-supervisée, le choix de modèle et l’estimation des paramètres de la texture et, finalement,3. la troisième méthode déconvolue et segmente une image composée de plusieurs régions texturées, en estimant au même temps les hyperparamètres (niveau du signal et niveau du bruit) et les paramètres de chaque texture.La contribution sur le plan algorithmique est représentée par une nouvelle version rapide de l’algorithme Metropolis-Hastings. Cet algorithme est basé sur une loi de proposition directionnelle contenant le terme de la ”direction de Newton”. Ce terme permet une exploration rapide et efficace de l’espace des paramètres et, de ce fait, accélère la convergence.
This thesis is addressing a series of inverse problems of major importance in the fieldof image processing (image segmentation, model choice, parameter estimation, deconvolution)in the context of textured images. In all of the aforementioned problems theobservations are indirect, i.e., the textured images are affected by a blur and by noise. Thecontributions of this work belong to three main classes: modeling, methodological andalgorithmic. From the modeling standpoint, the contribution consists in the development of a newnon-Gaussian model for textures. The Fourier coefficients of the textured images are modeledby a Scale Mixture of Gaussians Random Field. The Power Spectral Density of thetexture has a parametric form, driven by a set of parameters that encode the texture characteristics.The methodological contribution is threefold and consists in solving three image processingproblems that have not been tackled so far in the context of indirect observationsof textured images. All the proposed methods are Bayesian and are based on the exploitingthe information encoded in the a posteriori law. The first method that is proposed is devotedto the myopic deconvolution of a textured image and the estimation of its parameters.The second method achieves joint model selection and model parameters…
Advisors/Committee Members: Giovannelli, Jean-François (thesis director), Berthoumieu, Yannick (thesis director).
Subjects/Keywords: Problème inverse; BAYES; Segmentation; Hyper-paramètre; Déconvolution; Inverse problems; BAYES; Segmentation; Hyper-parameters; Deconvolution
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APA (6th Edition):
Văcar, C. P. (2014). Inversion for textured images : unsupervised myopic deconvolution, model selection, deconvolution-segmentation : Inversion pour image texturée : déconvolution myope non supervisée, choix de modèles, déconvolution-segmentation. (Doctoral Dissertation). Bordeaux. Retrieved from http://www.theses.fr/2014BORD0131
Chicago Manual of Style (16th Edition):
Văcar, Cornelia Paula. “Inversion for textured images : unsupervised myopic deconvolution, model selection, deconvolution-segmentation : Inversion pour image texturée : déconvolution myope non supervisée, choix de modèles, déconvolution-segmentation.” 2014. Doctoral Dissertation, Bordeaux. Accessed March 01, 2021.
http://www.theses.fr/2014BORD0131.
MLA Handbook (7th Edition):
Văcar, Cornelia Paula. “Inversion for textured images : unsupervised myopic deconvolution, model selection, deconvolution-segmentation : Inversion pour image texturée : déconvolution myope non supervisée, choix de modèles, déconvolution-segmentation.” 2014. Web. 01 Mar 2021.
Vancouver:
Văcar CP. Inversion for textured images : unsupervised myopic deconvolution, model selection, deconvolution-segmentation : Inversion pour image texturée : déconvolution myope non supervisée, choix de modèles, déconvolution-segmentation. [Internet] [Doctoral dissertation]. Bordeaux; 2014. [cited 2021 Mar 01].
Available from: http://www.theses.fr/2014BORD0131.
Council of Science Editors:
Văcar CP. Inversion for textured images : unsupervised myopic deconvolution, model selection, deconvolution-segmentation : Inversion pour image texturée : déconvolution myope non supervisée, choix de modèles, déconvolution-segmentation. [Doctoral Dissertation]. Bordeaux; 2014. Available from: http://www.theses.fr/2014BORD0131
Colorado State University
28.
Alsaker, Melody.
Computational advancements in the D-bar reconstruction method for 2-D electrical impedance tomography.
Degree: PhD, Mathematics, 2016, Colorado State University
URL: http://hdl.handle.net/10217/173372
► We study the problem of reconstructing 2-D conductivities from boundary voltage and current density measurements, also known as the electrical impedance tomography (EIT) problem, using…
(more)
▼ We study the problem of reconstructing 2-D conductivities from boundary voltage and current density measurements, also known as the electrical impedance tomography (EIT) problem, using the D-bar inversion method, based on the 1996 global uniqueness proof by Adrian Nachman. We focus on the computational implementation and efficiency of the D-bar algorithm, its application to finite-precision practical data in human thoracic imaging, and the quality and spatial resolution of the resulting reconstructions. The main contributions of this work are (1) a parallelized computational implementation of the algorithm which has been shown to run in real-time, thus demonstrating the feasibility of the D-bar method for use in real-time bedside imaging, and (2) a modification of the algorithm to include \emph{a priori} data in the form of approximate organ boundaries and (optionally) conductivity estimates, which we show to be effective in improving spatial resolution in the resulting reconstructions. These computational advancements are tested using both numerically simulated data as well as experimental human and tank data collected using the ACE1 EIT machine at CSU. In this work, we provide details regarding the theoretical background and practical implementation for each advancement, we demonstrate the effectiveness of the algorithm modifications through multiple experiments, and we provide discussion and conclusions based on the results.
Advisors/Committee Members: Mueller, Jennifer L. (advisor), Cheney, Margaret (committee member), Notaros, Branislav (committee member), Pinaud, Olivier (committee member).
Subjects/Keywords: electrical impedance tomography; inverse problems; D-bar algorithm; medical imaging; inverse conductivity problem
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APA (6th Edition):
Alsaker, M. (2016). Computational advancements in the D-bar reconstruction method for 2-D electrical impedance tomography. (Doctoral Dissertation). Colorado State University. Retrieved from http://hdl.handle.net/10217/173372
Chicago Manual of Style (16th Edition):
Alsaker, Melody. “Computational advancements in the D-bar reconstruction method for 2-D electrical impedance tomography.” 2016. Doctoral Dissertation, Colorado State University. Accessed March 01, 2021.
http://hdl.handle.net/10217/173372.
MLA Handbook (7th Edition):
Alsaker, Melody. “Computational advancements in the D-bar reconstruction method for 2-D electrical impedance tomography.” 2016. Web. 01 Mar 2021.
Vancouver:
Alsaker M. Computational advancements in the D-bar reconstruction method for 2-D electrical impedance tomography. [Internet] [Doctoral dissertation]. Colorado State University; 2016. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/10217/173372.
Council of Science Editors:
Alsaker M. Computational advancements in the D-bar reconstruction method for 2-D electrical impedance tomography. [Doctoral Dissertation]. Colorado State University; 2016. Available from: http://hdl.handle.net/10217/173372
University of New South Wales
29.
Marjanovic, Goran.
lq sparse signal estimation with applications.
Degree: Electrical Engineering & Telecommunications, 2012, University of New South Wales
URL: http://handle.unsw.edu.au/1959.4/52400
;
https://unsworks.unsw.edu.au/fapi/datastream/unsworks:11073/SOURCE01?view=true
► The use of sparsity has emerged in the last fifteen years as an important tool for solving many problems in the areas of signal processing…
(more)
▼ The use of sparsity has emerged in the last fifteen years as an important tool for solving many
problems in the areas of signal processing and statisticalinference. In this dissertation we pursue three significant applications of sparsity; sparse linear regression, low rank matrix completion and sparseinverse covariance selection. In the first and third topic, sparsity refers to having a small number of nonzero vector and matrix entries respectively,while in the second topic it is associated with low matrix rank.A penalized approach is considered involving optimization of an objective function with two terms. One of the terms measures the goodness of fit i.e.the error between the observed data and the estimated solution, while the other is a penalty responsible for inducing sparse solutions, hence the namepenalized problem.It is well understood that the natural way of inducing sparsity is through the l0 ``norm'' i.e. the counting function or the discrete metric. Since the l0function is non convex, a large volume of literature has instead resorted to using the convex l1 norm as the penalty. Therefore, the failure to consider thel0 penalized problem is a point of departure for this dissertation. In order to bridge the gap between the l0 and l1 penalties, the focus becomes thedevelopment of non convex optimization methods for the lq (0<q<1) penalized problem.Chapters 1 and 2 provide and describe the motivation and technical background respectively.Chapter 3 considers the topic of sparse linear regression, where we develop a nonlinear conjugate gradient algorithm for optimizing a smoothed lqpenalized least squares problem. The algorithm is applicable to any q>0 but the emphasis is on 0<q<1. Imposing basic assumptions, we prove that theiterates converge to a stationary point, and if this point is a local minimizer then it is also proved that the convergence is R-linear. Simulations are giventhat illustrate the potential of considering the use of our algorithm.Chapter 4 considers the topic of low rank matrix completion, where we develop an algorithm for optimizing an lq (rank) penalized least squares problemwith 0<q<1. In the development process we solve a non-trivial one dimensional lq optimization problem that is fundamental to our work. Additionally, ageneral algorithm convergence (fixed point) result with a non-trivial proof is given for 0≤q<1. We illustrate with data analysis examples, comparing thereconstruction quality of three matrix singular value penalties: l0, l1 and lq, 0<q<1.Chapter 5 considers the topic of sparse
inverse covariance estimation, where we develop an algorithm for optimizing an lq penalized log-likelihoodproblem with 0≤q<1. The development requires the solutions of the one dimensional lq optimization problem from Chapter 4. These are additionallyused to prove some algorithm properties as well as some fixed point results. We illustrate with simulations and a real world application example.Reconstruction comparisons are given using four penalties: l0, l1, lq with 0<q<1, and SCAD.Both,…
Advisors/Committee Members: Solo, Victor, Electrical Engineering & Telecommunications, Faculty of Engineering, UNSW.
Subjects/Keywords: Inverse problems; Sparse; Non convex; Matrix completion; Inverse covariance; Linear regression; Penalized problem
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Export
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APA (6th Edition):
Marjanovic, G. (2012). lq sparse signal estimation with applications. (Doctoral Dissertation). University of New South Wales. Retrieved from http://handle.unsw.edu.au/1959.4/52400 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:11073/SOURCE01?view=true
Chicago Manual of Style (16th Edition):
Marjanovic, Goran. “lq sparse signal estimation with applications.” 2012. Doctoral Dissertation, University of New South Wales. Accessed March 01, 2021.
http://handle.unsw.edu.au/1959.4/52400 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:11073/SOURCE01?view=true.
MLA Handbook (7th Edition):
Marjanovic, Goran. “lq sparse signal estimation with applications.” 2012. Web. 01 Mar 2021.
Vancouver:
Marjanovic G. lq sparse signal estimation with applications. [Internet] [Doctoral dissertation]. University of New South Wales; 2012. [cited 2021 Mar 01].
Available from: http://handle.unsw.edu.au/1959.4/52400 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:11073/SOURCE01?view=true.
Council of Science Editors:
Marjanovic G. lq sparse signal estimation with applications. [Doctoral Dissertation]. University of New South Wales; 2012. Available from: http://handle.unsw.edu.au/1959.4/52400 ; https://unsworks.unsw.edu.au/fapi/datastream/unsworks:11073/SOURCE01?view=true
King Abdullah University of Science and Technology
30.
Sandhu, Ali Imran.
Efficient and Accurate Numerical Techniques for Sparse Electromagnetic Imaging.
Degree: Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, 2020, King Abdullah University of Science and Technology
URL: http://hdl.handle.net/10754/662627
► Electromagnetic (EM) imaging schemes are inherently non-linear and ill-posed. Albeit there exist remedies to these fundamental problems, more efficient solutions are still being sought. To…
(more)
▼ Electromagnetic (EM) imaging schemes are inherently non-linear and ill-posed. Albeit there exist remedies to these fundamental
problems, more efficient solutions are still being sought. To this end, in this thesis, the non-linearity is tackled in- corporating a multitude of techniques (ranging from Born approximation (linear), inexact Newton (linearized) to complete nonlinear iterative Landweber schemes) that can account for weak to strong scattering
problems. The ill-posedness of the EM
inverse scattering problem is circumvented by formulating the above methods into a minimization problem with a sparsity constraint. More specifically, four novel in- verse scattering schemes are formulated and implemented. (i) A greedy algorithm is used together with a simple artificial neural network (ANN) for efficient and accu- rate EM imaging of weak scatterers. The ANN is used to predict the sparsity level of the investigation domain which is then used as the L0 - constraint parameter for the greedy algorithm. (ii) An inexact Newton scheme that enforces the sparsity con- straint on the derivative of the unknown material properties (not necessarily sparse) is proposed. The
inverse scattering problem is formulated as a nonlinear function of the derivative of the material properties. This approach results in significant spar- sification where any sparsity regularization method could be efficiently applied. (iii) A sparsity regularized nonlinear contrast source (CS) framework is developed to di- rectly solve the nonlinear minimization problem using Landweber iterations where the convergence is accelerated using a self-adaptive projected accelerated steepest
descent algorithm. (iv) A 2.5D finite difference frequency domain (FDFD) based in-
verse scattering scheme is developed for imaging scatterers embedded in lossy and inhomogeneous media. The FDFD based inversion algorithm does not require the Green’s function of the background medium and appears a promising technique for biomedical and subsurface imaging with a reasonable computational time.
Numerical experiments, which are carried out using synthetically generated mea- surements, show that the images recovered by these sparsity-regularized methods are sharper and more accurate than those produced by existing methods. The methods developed in this work have potential application areas ranging from oil/gas reservoir engineering to biological imaging where sparse domains naturally exist.
Advisors/Committee Members: Bagci, Hakan (advisor), Ooi, Boon S. (committee member), Hoteit, Ibrahim (committee member), Dorn, Oliver (committee member).
Subjects/Keywords: Electromagnetic inverse scattering; Inverse problems; Sparsity regularization; Microwave imaging; Accelerated steepest descent; Artificial neural network
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APA (6th Edition):
Sandhu, A. I. (2020). Efficient and Accurate Numerical Techniques for Sparse Electromagnetic Imaging. (Thesis). King Abdullah University of Science and Technology. Retrieved from http://hdl.handle.net/10754/662627
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Chicago Manual of Style (16th Edition):
Sandhu, Ali Imran. “Efficient and Accurate Numerical Techniques for Sparse Electromagnetic Imaging.” 2020. Thesis, King Abdullah University of Science and Technology. Accessed March 01, 2021.
http://hdl.handle.net/10754/662627.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
MLA Handbook (7th Edition):
Sandhu, Ali Imran. “Efficient and Accurate Numerical Techniques for Sparse Electromagnetic Imaging.” 2020. Web. 01 Mar 2021.
Vancouver:
Sandhu AI. Efficient and Accurate Numerical Techniques for Sparse Electromagnetic Imaging. [Internet] [Thesis]. King Abdullah University of Science and Technology; 2020. [cited 2021 Mar 01].
Available from: http://hdl.handle.net/10754/662627.
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
Council of Science Editors:
Sandhu AI. Efficient and Accurate Numerical Techniques for Sparse Electromagnetic Imaging. [Thesis]. King Abdullah University of Science and Technology; 2020. Available from: http://hdl.handle.net/10754/662627
Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation
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Open Access Theses and Dissertations
