subject:(inverse problem)

Johannes Gutenberg Universität Mainz

1. Hollborn, Stefanie. Ein inverses Rückstreuproblem der elektrischen Impedanztomographie.

Degree: 2012, Johannes Gutenberg Universität Mainz

URL: http://ubm.opus.hbz-nrw.de/volltexte/2012/3218/

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Die vorliegende Arbeit untersucht das inverse Hindernisproblem der zweidimensionalen elektrischen Impedanztomographie (EIT) mit Rückstreudaten. Wir präsentieren und analysieren das mathematische Modell für Rückstreudaten, diskutieren das… (more)

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Die vorliegende Arbeit untersucht das inverse Hindernisproblem der zweidimensionalen elektrischen Impedanztomographie (EIT) mit Rückstreudaten. Wir präsentieren und analysieren das mathematische Modell für Rückstreudaten, diskutieren das inverse Problem für einen einzelnen isolierenden oder perfekt leitenden Einschluss und stellen zwei Rekonstruktionsverfahren für das inverse Hindernisproblem mit Rückstreudaten vor. Ziel des inversen Hindernisproblems der EIT ist es, Inhomogenitäten (sogenannte Einschlüsse) der elektrischen Leitfähigkeit eines Körpers aus Strom-Spannungs-Messungen an der Körperoberfläche zu identifizieren. Für die Messung von Rückstreudaten ist dafür nur ein Paar aus an der Körperoberfläche nahe zueinander angebrachten Elektroden nötig, das zur Datenerfassung auf der Oberfläche entlang bewegt wird. Wir stellen ein mathematisches Modell für Rückstreudaten vor und zeigen, dass Rückstreudaten die Randwerte einer außerhalb der Einschlüsse holomorphen Funktion sind. Auf dieser Grundlage entwickeln wir das Konzept des konvexen Rückstreuträgers: Der konvexe Rückstreuträger ist eine Teilmenge der konvexen Hülle der Einschlüsse und kann daher zu deren Auffindung dienen. Wir stellen einen Algorithmus zur Berechnung des konvexen Rückstreuträgers vor und demonstrieren ihn an numerischen Beispielen. Ferner zeigen wir, dass ein einzelner isolierender Einschluss anhand seiner Rückstreudaten eindeutig identifizierbar ist. Der Beweis dazu beruht auf dem Riemann'schen Abbildungssatz für zweifach zusammenhängende Gebiete und dient als Grundlage für einen Rekonstruktionsalgorithmus, dessen Leistungsfähigkeit wir an verschiedenen Beispielen demonstrieren. Ein perfekt leitender Einschluss ist hingegen nicht immer aus seinen Rückstreudaten rekonstruierbar. Wir diskutieren, in welchen Fällen die eindeutige Identifizierung fehlschlägt und zeigen Beispiele für unterschiedliche perfekt leitende Einschlüsse mit gleichen Rückstreudaten.

The present thesis investigates the inverse obstacle problem of two-dimensional impedance tomography with backscatter data. We present and analyze the mathematical model for backscatter data and we discuss the inverse problem for a single insulating or perfectly conducting inclusion. Furthermore, we introduce two reconstruction algorithms for the inverse obstacle problem. The aim of the inverse obstacle problem in impedance tomography is to identify inhomogeneities in the electric conductivity of a physical body by means of current-voltage-measurements at the object's boundary. For the acquisition of backscatter data, only a single pair of closely adjacent electrodes is necessary that is moved along the object's boundary recording data. We present a mathematical model for backscatter data and we show that backscatter data are the boundary values of a function that is holomorphic in the exterior of the inclusions. On this basis we develop the concept of the convex backscattering support: The convex backscattering support is a subset of the convex hull of the inclusions and hence gives evidence…

Subjects/Keywords: inverses Problem; inverse problem; Mathematics

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APA (6^th Edition):

Hollborn, S. (2012). Ein inverses Rückstreuproblem der elektrischen Impedanztomographie. (Doctoral Dissertation). Johannes Gutenberg Universität Mainz. Retrieved from http://ubm.opus.hbz-nrw.de/volltexte/2012/3218/

Chicago Manual of Style (16^th Edition):

Hollborn, Stefanie. “Ein inverses Rückstreuproblem der elektrischen Impedanztomographie.” 2012. Doctoral Dissertation, Johannes Gutenberg Universität Mainz. Accessed March 01, 2021. http://ubm.opus.hbz-nrw.de/volltexte/2012/3218/.

MLA Handbook (7^th Edition):

Hollborn, Stefanie. “Ein inverses Rückstreuproblem der elektrischen Impedanztomographie.” 2012. Web. 01 Mar 2021.

Vancouver:

Hollborn S. Ein inverses Rückstreuproblem der elektrischen Impedanztomographie. [Internet] [Doctoral dissertation]. Johannes Gutenberg Universität Mainz; 2012. [cited 2021 Mar 01]. Available from: http://ubm.opus.hbz-nrw.de/volltexte/2012/3218/.

Council of Science Editors:

Hollborn S. Ein inverses Rückstreuproblem der elektrischen Impedanztomographie. [Doctoral Dissertation]. Johannes Gutenberg Universität Mainz; 2012. Available from: http://ubm.opus.hbz-nrw.de/volltexte/2012/3218/

Université de Bordeaux I

2. Lopez Rincon, Alejandro. Le problème inverse en l'électrocardiographie : The resolution of the inverse problem in electrocardiography.

Degree: Docteur es, Mathématiques appliquées, 2013, Université de Bordeaux I

URL: http://www.theses.fr/2013BOR15261

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Dans le problème inverse d’électrocardiographie, le cible est faire la reconstruction de l’activité électrophysiologique dans le cœur sans mesurer directement dans sa surface (sans interventions… (more)

Subjects/Keywords: Problème inverse; Electrocardiographie; Inverse problem; Electrocardiography

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APA (6^th Edition):

Lopez Rincon, A. (2013). Le problème inverse en l'électrocardiographie : The resolution of the inverse problem in electrocardiography. (Doctoral Dissertation). Université de Bordeaux I. Retrieved from http://www.theses.fr/2013BOR15261

Chicago Manual of Style (16^th Edition):

Lopez Rincon, Alejandro. “Le problème inverse en l'électrocardiographie : The resolution of the inverse problem in electrocardiography.” 2013. Doctoral Dissertation, Université de Bordeaux I. Accessed March 01, 2021. http://www.theses.fr/2013BOR15261.

MLA Handbook (7^th Edition):

Lopez Rincon, Alejandro. “Le problème inverse en l'électrocardiographie : The resolution of the inverse problem in electrocardiography.” 2013. Web. 01 Mar 2021.

Vancouver:

Lopez Rincon A. Le problème inverse en l'électrocardiographie : The resolution of the inverse problem in electrocardiography. [Internet] [Doctoral dissertation]. Université de Bordeaux I; 2013. [cited 2021 Mar 01]. Available from: http://www.theses.fr/2013BOR15261.

Council of Science Editors:

Lopez Rincon A. Le problème inverse en l'électrocardiographie : The resolution of the inverse problem in electrocardiography. [Doctoral Dissertation]. Université de Bordeaux I; 2013. Available from: http://www.theses.fr/2013BOR15261

3. Nummenmaa, Aapo. Hierarchical Bayesian Aspects of Distributed Neuromagnetic Source Models.

Degree: 2008, Helsinki University of Technology

URL: http://lib.tkk.fi/Diss/2008/isbn9789512291434/

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Magnetoencephalography (MEG) enables noninvasive measurements of cerebral activity with excellent temporal resolution, but localising the neural currents generating the extracranial magnetic fields admits no unique… (more)

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Magnetoencephalography (MEG) enables noninvasive measurements of cerebral activity with excellent temporal resolution, but localising the neural currents generating the extracranial magnetic fields admits no unique solution. By imposing some mathematical constraints on the currents, reasonable solutions to this electromagnetic inverse problem can be obtained. In this work, we adopt the statistical formulation of the inverse problem in which the constraints are encoded as Bayesian prior probabilities. The prior is combined with a statistical MEG observation model via Bayes' theorem to yield the posterior probability of the unknown parameters, that is the currents, given the MEG data and modeling assumptions. Apart from the currents, the prior probability density may contain further parameters which are subject to uncertainty. These parameters are not related directly to the MEG observations and are called second-level parameters or hyperparameters, giving the model a hierarchical structure. The thesis considers hierarchical generalisations of the classical Minimum-Norm and Minimum-Current Estimates (MNE and MCE). The MNE and MCE are distributed source reconstruction methods from which the former is known to produce spatially diffuse distributions and the latter more focal. The here studied extensions of the MNE and MCE prior structures allow more general and flexible modeling of distributed sources with properties in between MNE and MCE. The first two studies included in this thesis involve more theoretical Bayesian analyses on the properties of the hierarchical distributed source models and the resulting inverse estimates. The latter two studies focus on validation of the models with empirical MEG data, practical analyses and interpretation of the inverse estimates.

Magnetoenkefalografia (MEG) mahdollistaa pään ulkopuolelta tapahtuvan aivotoimintojen mittaamisen hyvällä ajallisella tarkkuudella, mutta nämä magneettikentät synnyttävien aivokudoksen sähkövirtojen paikallistaminen vaatii ns. sähkömagneettisen käänteisongelman ratkaisun, joka ei ole yksikäsitteinen. Jos virtakonfiguraatioille asetetaan sopivia matemaattisia rajoitteita, on kuitenkin mahdollista löytää käyttökelpoisia ratkaisuja tähän käänteisongelmaan. Tässä työssä käänteisongelmaa lähestytään tilastollisesti, ja matemaattiset rajoitteet muotoillaan Bayesilaisittain a priori todennäköisyyksinä. Tämä priorijakauma yhdistetään tilastollisen MEG-havaintomallin kanssa, jolloin saadaan Bayesin teoreeman avulla tuntemattomien parametrien eli virtakonfiguraatioiden a posteriori -jakauma, joka kertoo eri virtakonfiguraatioden todennäköisyydet, annettuna havaittu data sekä tehdyt mallioletukset. Virtojen lisäksi priorijakaumaan saattaa liittyä muita tuntemattomia suureita, jotka sisältävät epävarmuutta. Nämä parametrit eivät kytkeydy suoraan MEG-mittauksiin, joten ne ovat siis sähkövirtoihin verrattuna seuraavalla mallitasolla. Näitä priorin parametreja kutsutaan hyperparametreiksi, ja mallilla on hierarkinen rakenne. Väitöskirjassa tutkitaan klassisten…

Advisors/Committee Members: Helsinki University of Technology, Department of Electrical and Communications Engineering, Laboratory of Computational Engineering.

Subjects/Keywords: magnetoencephalography; inverse problem; Bayesian analysis

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APA (6^th Edition):

Nummenmaa, A. (2008). Hierarchical Bayesian Aspects of Distributed Neuromagnetic Source Models. (Thesis). Helsinki University of Technology. Retrieved from http://lib.tkk.fi/Diss/2008/isbn9789512291434/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Nummenmaa, Aapo. “Hierarchical Bayesian Aspects of Distributed Neuromagnetic Source Models.” 2008. Thesis, Helsinki University of Technology. Accessed March 01, 2021. http://lib.tkk.fi/Diss/2008/isbn9789512291434/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Nummenmaa, Aapo. “Hierarchical Bayesian Aspects of Distributed Neuromagnetic Source Models.” 2008. Web. 01 Mar 2021.

Vancouver:

Nummenmaa A. Hierarchical Bayesian Aspects of Distributed Neuromagnetic Source Models. [Internet] [Thesis]. Helsinki University of Technology; 2008. [cited 2021 Mar 01]. Available from: http://lib.tkk.fi/Diss/2008/isbn9789512291434/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Nummenmaa A. Hierarchical Bayesian Aspects of Distributed Neuromagnetic Source Models. [Thesis]. Helsinki University of Technology; 2008. Available from: http://lib.tkk.fi/Diss/2008/isbn9789512291434/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Cornell University

4. Aguilo, Miguel. Inverse Strategies For Characterization Of Material Properties.

Degree: PhD, Civil and Environmental Engineering, 2011, Cornell University

URL: http://hdl.handle.net/1813/33569

► The imaging of constitutive parameters is of interest in many science and engineering fields. Indeed, non-invasive and nondestructive techniques are used to characterize key properties… (more)

▼ The imaging of constitutive parameters is of interest in many science and engineering fields. Indeed, non-invasive and nondestructive techniques are used to characterize key properties of a system given its response due to an external excitation. Then, assuming a priori a given model of the system, the measured response and an inverse approach are used to identify material properties. This work was undertaken in the context of identification of spatially-varying elastic and viscoelastic parameters of solids using vibroacoustics based techniques. Two optimization approaches, nongradient and gradient-based optimization, were investigated in this work. Initially, nongradient-based algorithms were preferred over gradient-based algorithms because of there ability to find global minima irrespective of initial guesses. For instance, Gaussian radial basis functions were used to construct a finite-dimensional representation of the elastic moduli. Then, an inverse approach was used to approximate the spatiallyvarying elastic moduli through the system response induced by the radiation force of ultrasound. The inverse problem was cast as an optimization problem in which a least-square error functional that quantified the misfit between the experimental and finite element representation system response is minimized by searching over a space of admissible vectors that best describe the spatial distribution of the elastic moduli. Subsequently, gradient-based optimization was preferred over nongradient-based optimization as the number of design variables increased due to the increment in computational cost. Two inverse approaches, L2-adjoint and concept of error in constitutive equation, were investigated in the context of gradient-based optimization. First, the L2-adjoint inverse approach was used to characterize spatially-varying viscoelastic properties because of its advantage to efficiently calculate the gradient of the error functional with respect to the design variables by solving the corresponding adjoint equations. The inverse problem was cast as an optimization problem in which a least-square error functional that quantified the misfit between the experimental and the finite element representation system response is minimized by searching over a space of admissible functions that best describe the spatially-varying viscoelastic properties. Given that the least-square error functional is non-convex, an inverse approach based on the concept of error in constitutive equation was investigated. The convexity property of the error in constitutive equation functionals, shown extensively for elliptic boundary value problems, reduce the sensitivity of the inverse solution to parameter initialization. The inverse problem was cast as an optimization problem in which an error in constitutive equation functional that quantified the misfit between the kinematically and dynamically admissible stress fields is minimized by searching over a space of admissible functions that best describe the spatially-varying viscoelastic properties.… Advisors/Committee Members: Aquino, Wilkins (chair), Mukherjee, Subrata (committee member), Ingraffea, Anthony R (committee member), Bonassar, Lawrence (committee member).

Subjects/Keywords: viscoelasticity imaging; inverse problem; vibroacoustography

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APA (6^th Edition):

Aguilo, M. (2011). Inverse Strategies For Characterization Of Material Properties. (Doctoral Dissertation). Cornell University. Retrieved from http://hdl.handle.net/1813/33569

Chicago Manual of Style (16^th Edition):

Aguilo, Miguel. “Inverse Strategies For Characterization Of Material Properties.” 2011. Doctoral Dissertation, Cornell University. Accessed March 01, 2021. http://hdl.handle.net/1813/33569.

MLA Handbook (7^th Edition):

Aguilo, Miguel. “Inverse Strategies For Characterization Of Material Properties.” 2011. Web. 01 Mar 2021.

Vancouver:

Aguilo M. Inverse Strategies For Characterization Of Material Properties. [Internet] [Doctoral dissertation]. Cornell University; 2011. [cited 2021 Mar 01]. Available from: http://hdl.handle.net/1813/33569.

Council of Science Editors:

Aguilo M. Inverse Strategies For Characterization Of Material Properties. [Doctoral Dissertation]. Cornell University; 2011. Available from: http://hdl.handle.net/1813/33569

Texas A&M University

5. Nam, Haewon. Ultrasound-modulated optical tomography.

Degree: PhD, Mathematics, 2004, Texas A&M University

URL: http://hdl.handle.net/1969.1/448

► Ultrasound-modulated optical tomography is modeled by a linear integral equation and an inverse problem involving a diffusion equation in n spatial dimensions, n=2, 3. Based… (more)

Subjects/Keywords: Inverse Problem

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APA (6^th Edition):

Nam, H. (2004). Ultrasound-modulated optical tomography. (Doctoral Dissertation). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/448

Chicago Manual of Style (16^th Edition):

Nam, Haewon. “Ultrasound-modulated optical tomography.” 2004. Doctoral Dissertation, Texas A&M University. Accessed March 01, 2021. http://hdl.handle.net/1969.1/448.

MLA Handbook (7^th Edition):

Nam, Haewon. “Ultrasound-modulated optical tomography.” 2004. Web. 01 Mar 2021.

Vancouver:

Nam H. Ultrasound-modulated optical tomography. [Internet] [Doctoral dissertation]. Texas A&M University; 2004. [cited 2021 Mar 01]. Available from: http://hdl.handle.net/1969.1/448.

Council of Science Editors:

Nam H. Ultrasound-modulated optical tomography. [Doctoral Dissertation]. Texas A&M University; 2004. Available from: http://hdl.handle.net/1969.1/448

University of Hawaii – Manoa

6. Billings, Paul Allen. Positivity constraint implementations for multiframe blind deconvolution reconstructions.

Degree: 2015, University of Hawaii – Manoa

URL: http://hdl.handle.net/10125/101055

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Ph.D. University of Hawaii at Manoa 2014.

Reconstruction of imagery degraded by atmospheric turbulence is inherently an ill-posed problem. Multiple solutions can be found which… (more)

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Ph.D. University of Hawaii at Manoa 2014.

Reconstruction of imagery degraded by atmospheric turbulence is inherently an ill-posed problem. Multiple solutions can be found which satisfy the measured data to the extent allowed by the noise statistics. The symmetric nature of a spatially invariant imaging system gives rise to an ambiguity between object and distortion. Furthermore, portions of the object spatial frequency information are often attenuated beyond usefulness. Research in this field is primarily concerned with resolving this ambiguity and making a quality estimate of the object in a timely fashion. Many of the more advanced image reconstruction algorithms are iterative algorithms, seeking to minimize error/cost or maximize likelihood/conditional probability. The estimates, of course, are random variables, and regularization and constraints are often employed to guide solutions or reduce effects of overfitting. While positivity is an often employed constraint, one can conceive of various ways to achieve this beyond the typical approach of squaring the search parameters. We evaluate several functional parameterizations as well as the use of an optimizer employing search boundaries. We also consider the order of application in conjunction with a smoothness constraint. Performance is quantified by metrics, including RMS error (spatial domain), RMS phase error curves (spatial frequency domain), and timing to characterize computational demands. We find the RMS phase error curves to be the most valuable as they assess reconstruction accuracy as a function of level of detail. Of the parameterizations evaluated, implementation of object positivity through squaring the parameters prior to application of a smoothness constraint achieved the best blend of accuracy and runtime execution speed. Development of the theoretical background in a common framework contributed to reuse of constituent quantities, both in the development of the likelihood and many gradient expressions as well as implementation of those expressions into computer code. Such reuse promotes accuracy as well as ease of new development.

Subjects/Keywords: parameterization; inverse problem; deconvolution

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APA (6^th Edition):

Billings, P. A. (2015). Positivity constraint implementations for multiframe blind deconvolution reconstructions. (Thesis). University of Hawaii – Manoa. Retrieved from http://hdl.handle.net/10125/101055

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Billings, Paul Allen. “Positivity constraint implementations for multiframe blind deconvolution reconstructions.” 2015. Thesis, University of Hawaii – Manoa. Accessed March 01, 2021. http://hdl.handle.net/10125/101055.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Billings, Paul Allen. “Positivity constraint implementations for multiframe blind deconvolution reconstructions.” 2015. Web. 01 Mar 2021.

Vancouver:

Billings PA. Positivity constraint implementations for multiframe blind deconvolution reconstructions. [Internet] [Thesis]. University of Hawaii – Manoa; 2015. [cited 2021 Mar 01]. Available from: http://hdl.handle.net/10125/101055.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Billings PA. Positivity constraint implementations for multiframe blind deconvolution reconstructions. [Thesis]. University of Hawaii – Manoa; 2015. Available from: http://hdl.handle.net/10125/101055

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Clemson University

7. Brinckerhoff, Matthew. Comparison of Electrical Impedance Tomography Reconstruction Algorithms With EIDORS Reconstruction Software.

Degree: MS, Mathematical Sciences, 2018, Clemson University

URL: https://tigerprints.clemson.edu/all_theses/2973

► Electrical impedance tomography ("EIT") has many significant applications, ranging from geophysical and medical imaging, to the military, to industrial fields. Due to the relevance of… (more)

▼ Electrical impedance tomography ("EIT") has many significant applications, ranging from geophysical and medical imaging, to the military, to industrial fields. Due to the relevance of EIT in fields of critical importance to society, further development of EIT is vital. The instability of image reconstruction and the highly nonlinear behavior of the image reconstruction problem, make the problem particularly difficult, are referred to as ill-posed inverse problem. Specifically, development of a comprehensive set of techniques to solve the EIT problem is necessary, due to both its ill-posed, nonlinear nature, and its scope. In this thesis, several approaches to the inversion of the EIT problem are presented, as well as a comparison with the inversion software EIDORS (Electrical Impedance Tomography and Diffuse Optical Tomography Reconstruction Software). In this thesis, the advantages and disadvantages of EIT as compared to other imaging techniques is discussed. Then the theory of EIT, including the governing equations, the forward problem, and methods for solving the inverse problem are presented. Next, the reconstruction software EIDORS is presented, in which artificial data is created, and the reconstruction algorithms are implemented. The effect of noise on the simulated data is investigated. Lastly, experimental data is implemented, and the results are discussed. We considered absolute conductivities in reconstruction, which was a gap in previous work, and have thus resolved this missing element of the work. The experimental data was successfully reconstructed with two different absolute reconstruction algorithms. Additionally, the optimal injection patterns were evaluated for accuracy and practical application. Lastly, we observed that the reconstruction algorithms were extremely sensitive to the regularization parameter, implying that the parameter selection method is of paramount importance. In this thesis, we have considered smoothness constraints such as TV regularization and L_2 regularization which leads to reasonable reconstruction using experimental data and leads the way for future comparison to sparsity and statistical approaches to solve the EIT inverse problem. Advisors/Committee Members: Dr. Taufiquar Khan, Committee Chair, Dr. Shitao Liu, Dr. Jeong Yoon.

Subjects/Keywords: Electrical Impedance Tomography; Inverse Problem

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APA (6^th Edition):

Brinckerhoff, M. (2018). Comparison of Electrical Impedance Tomography Reconstruction Algorithms With EIDORS Reconstruction Software. (Masters Thesis). Clemson University. Retrieved from https://tigerprints.clemson.edu/all_theses/2973

Chicago Manual of Style (16^th Edition):

Brinckerhoff, Matthew. “Comparison of Electrical Impedance Tomography Reconstruction Algorithms With EIDORS Reconstruction Software.” 2018. Masters Thesis, Clemson University. Accessed March 01, 2021. https://tigerprints.clemson.edu/all_theses/2973.

MLA Handbook (7^th Edition):

Brinckerhoff, Matthew. “Comparison of Electrical Impedance Tomography Reconstruction Algorithms With EIDORS Reconstruction Software.” 2018. Web. 01 Mar 2021.

Vancouver:

Brinckerhoff M. Comparison of Electrical Impedance Tomography Reconstruction Algorithms With EIDORS Reconstruction Software. [Internet] [Masters thesis]. Clemson University; 2018. [cited 2021 Mar 01]. Available from: https://tigerprints.clemson.edu/all_theses/2973.

Council of Science Editors:

Brinckerhoff M. Comparison of Electrical Impedance Tomography Reconstruction Algorithms With EIDORS Reconstruction Software. [Masters Thesis]. Clemson University; 2018. Available from: https://tigerprints.clemson.edu/all_theses/2973

King Abdullah University of Science and Technology

8. Asiri, Sharefa M. Modulating Function-Based Method for Parameter and Source Estimation of Partial Differential Equations.

Degree: Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, 2017, King Abdullah University of Science and Technology

URL: http://hdl.handle.net/10754/625846

► Partial Differential Equations (PDEs) are commonly used to model complex systems that arise for example in biology, engineering, chemistry, and elsewhere. The parameters (or coefficients)… (more)

▼ Partial Differential Equations (PDEs) are commonly used to model complex systems that arise for example in biology, engineering, chemistry, and elsewhere. The parameters (or coefficients) and the source of PDE models are often unknown and are estimated from available measurements. Despite its importance, solving the estimation problem is mathematically and numerically challenging and especially when the measurements are corrupted by noise, which is often the case. Various methods have been proposed to solve estimation problems in PDEs which can be classified into optimization methods and recursive methods. The optimization methods are usually heavy computationally, especially when the number of unknowns is large. In addition, they are sensitive to the initial guess and stop condition, and they suffer from the lack of robustness to noise. Recursive methods, such as observer-based approaches, are limited by their dependence on some structural properties such as observability and identifiability which might be lost when approximating the PDE numerically. Moreover, most of these methods provide asymptotic estimates which might not be useful for control applications for example. An alternative non-asymptotic approach with less computational burden has been proposed in engineering fields based on the so-called modulating functions. In this dissertation, we propose to mathematically and numerically analyze the modulating functions based approaches. We also propose to extend these approaches to different situations. The contributions of this thesis are as follows. (i) Provide a mathematical analysis of the modulating function-based method (MFBM) which includes: its well-posedness, statistical properties, and estimation errors. (ii) Provide a numerical analysis of the MFBM through some estimation problems, and study the sensitivity of the method to the modulating functions' parameters. (iii) Propose an effective algorithm for selecting the method's design parameters. (iv) Develop a two-dimensional MFBM to estimate space-time dependent unknowns which is illustrated in estimating the source term in the damped wave equation describing the physiological characterization of brain activity. (v) Introduce a moving horizon strategy in the MFBM for on-line estimation and examine its effectiveness on estimating the source term of a first order hyperbolic equation which describes the heat transfer in distributed solar collector systems. Advisors/Committee Members: Laleg-Kirati, Taous-Meriem (advisor), Keyes, David E. (committee member), Stenchikov, Georgiy L. (committee member), Wu, Ying (committee member), Avdonin, Sergei (committee member), Liu, Yan-Da (committee member).

Subjects/Keywords: Inverse problem; Estimation; modulating functions

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APA (6^th Edition):

Asiri, S. M. (2017). Modulating Function-Based Method for Parameter and Source Estimation of Partial Differential Equations. (Thesis). King Abdullah University of Science and Technology. Retrieved from http://hdl.handle.net/10754/625846

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Asiri, Sharefa M. “Modulating Function-Based Method for Parameter and Source Estimation of Partial Differential Equations.” 2017. Thesis, King Abdullah University of Science and Technology. Accessed March 01, 2021. http://hdl.handle.net/10754/625846.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Asiri, Sharefa M. “Modulating Function-Based Method for Parameter and Source Estimation of Partial Differential Equations.” 2017. Web. 01 Mar 2021.

Vancouver:

Asiri SM. Modulating Function-Based Method for Parameter and Source Estimation of Partial Differential Equations. [Internet] [Thesis]. King Abdullah University of Science and Technology; 2017. [cited 2021 Mar 01]. Available from: http://hdl.handle.net/10754/625846.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Asiri SM. Modulating Function-Based Method for Parameter and Source Estimation of Partial Differential Equations. [Thesis]. King Abdullah University of Science and Technology; 2017. Available from: http://hdl.handle.net/10754/625846

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Colorado State University

9. 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)

Subjects/Keywords: Calderon problem; inverse problems; inverse conductivity problem; D-bar

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APA (6^th 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 (16^th 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 (7^th 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

10. Auranen, Toni. Computational Methods for Bayesian Estimation of Neuromagnetic Sources.

Degree: 2007, Helsinki University of Technology

URL: http://lib.tkk.fi/Diss/2007/isbn9789512289547/

►

The electromagnetic inverse problem in human brain research consists of determining underlying source currents in the brain based on measurements outside the head. Solution to… (more)

▼

The electromagnetic inverse problem in human brain research consists of determining underlying source currents in the brain based on measurements outside the head. Solution to the inverse problem is ambiguous, necessitating the use of prior information and modeling assumptions for obtaining reasonable inverse estimates. In this study, we create new and improve existing computational methods for estimating neuromagnetic sources in the human brain. One straightforward way of incorporating presumptions to this problem is to formulate it in a probabilistic Bayesian manner. Bayesian statistics is largely based on modeling uncertainties associated with parameters constituting the model by representing them with probability distributions. In this work, existing neuroscientific knowledge and information from anatomical and functional magnetic resonance imaging are used as prior assumptions in model implementation. The neuromagnetic inverse problem is resolved with two different approaches. First, we perform the analysis using distributed source current modeling and infer some arbitrary parameter choices and the source currents from the measurement data by using numerical sampling methods. We apply similar strategies to cortically constrained current dipole localization and suggest using functional magnetic resonance imaging data for guiding the sampling algorithm. The models are tested with simulated and measured data. The presented methods are rather automatic, yielding plausible and robust inverse estimates of cortical current sources. With the spatiotemporal dipole localization model, the inclusion of functional magnetic resonance imaging data improves performance of the numerical sampling method. However, apparent multimodality of the parameter posterior distribution causes complications especially with empirical data. We suggest using loose cortical orientation constraints for smoothing down the complicated posterior distribution instead of marginal improvements to the sampling scheme. This might help to overcome the somewhat limited mixing properties of the sampling algorithm and ease the inconvenient multimodality of the posterior distribution.

Ihmisaivojen tutkimukseen liittyvällä sähkömagneettisella käänteisongelmalla tarkoitetaan aivojen virtalähteiden paikantamista pään ulkopuolisten mittausten perusteella. Ongelmaan ei ole yksikäsitteistä ratkaisua, joten mallintamisessa on käytettävä ennakko-oletuksia järkevien ratkaisujen tuottamiseksi. Tässä tutkimuksessa kehitämme uusia ja parannamme olemassaolevia laskennallisia menetelmiä aivoissa syntyvien magneettikenttiä tuottavien lähteiden paikantamiseksi. Kenties yksinkertaisin tapa lisätä ennakko-oletuksia tähän ongelmaan on käyttää bayesilaista mallintamista. Bayesilainen tilastotiede perustuu pitkälti parametrien epävarmuuksien mallintamiseen ja esittämiseen todennäköisyysjakaumin. Työn mallien muodostamisessa käytetään apuna aivojen toiminnallisesta ja rakenteellisesta magneettikuvauksesta saatavaa neurotieteellistä ennakkotietoa. Sähkömagneettisen…

Advisors/Committee Members: Helsinki University of Technology, Department of Electrical and Communications Engineering, Laboratory of Computational Engineering.

Subjects/Keywords: inverse problem; magnetoencephalography; Markov chain Monte Carlo

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Auranen, T. (2007). Computational Methods for Bayesian Estimation of Neuromagnetic Sources. (Thesis). Helsinki University of Technology. Retrieved from http://lib.tkk.fi/Diss/2007/isbn9789512289547/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Auranen, Toni. “Computational Methods for Bayesian Estimation of Neuromagnetic Sources.” 2007. Thesis, Helsinki University of Technology. Accessed March 01, 2021. http://lib.tkk.fi/Diss/2007/isbn9789512289547/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Auranen, Toni. “Computational Methods for Bayesian Estimation of Neuromagnetic Sources.” 2007. Web. 01 Mar 2021.

Vancouver:

Auranen T. Computational Methods for Bayesian Estimation of Neuromagnetic Sources. [Internet] [Thesis]. Helsinki University of Technology; 2007. [cited 2021 Mar 01]. Available from: http://lib.tkk.fi/Diss/2007/isbn9789512289547/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Auranen T. Computational Methods for Bayesian Estimation of Neuromagnetic Sources. [Thesis]. Helsinki University of Technology; 2007. Available from: http://lib.tkk.fi/Diss/2007/isbn9789512289547/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Penn State University

11. Yun, Xingzhao. RECONSTRUCTION OF ULTRASOUND TOMOGRAPHY FOR CANCER DETECTION USING ADVANCED REGULARIZATION METHODS.

Degree: 2019, Penn State University

URL: https://submit-etda.libraries.psu.edu/catalog/16034xuy43

► Tumors are common in human body, but it will be lethal when cancer cells invade important organs. Therefore early detection is necessary for cancer treatment.… (more)

▼ Tumors are common in human body, but it will be lethal when cancer cells invade important organs. Therefore early detection is necessary for cancer treatment. Ultrasound Tomography(UT), as a non-invasive technology, has been widely used in decades. The goal of UT is to reconstruct the inner object based on it’s physical properties according to wave propagation in inhomogeneous environment. Multiple transmitters and multiple receivers make it possible to collect more data for image reconstruction, however, the regularization method for ill-posed problem and computational consuming are still two main challenges in UT. This thesis shows the results of the modeling and reconstruction of UT imaging for different simulated phantoms. One of the powerful approach that has been widely used in UT is the Distorted Born Iteration Method(DBIM), which is a method that iteratively solves forward problem and inverse problem for the inhomogeneities in the Region of Interest (ROI). Forward problem contains two sub-problems, computing total field and estimating the inhomogeneous Green’s function. Inverse problem solves scattering function of inner objects. Forward model is a well-posed system which makes it easy to solve. On the other hand, the principal computational challenge involved is the solution for ill-posed inverse problem, therefore the whole problem is considered to be an inverse scattering problem for simplicity. The first part of this work deals with theoretical aspects of ultrasound tomography and DBIM method. The inhomogensous wave propagation frame was derived as the mathematical background. Inverse model, forward model and Green’s function work for a valid reconstruction procedure have been shown in this thesis. The second part of this thesis dedicates to the computational cost in ill-conditioned inverse scattering problem. The comparison of several regularization methods including Truncated Total Least Squares (TTLS), Conjugate Gradient Least Squares (CGLS), Tikhonov and v-method are shown in this work. The contrast sensitive problem with different domains and their reconstruction performance with various noise conditions are addressed as well. Furthermore, the pros and cons of underdetermined system and overdetermined system for different regularization methods are demonstrated. Finally, the simulation results and conclusions on different aspects of conditions are discussed. Advisors/Committee Members: Almekkawy Mohamed, Thesis Advisor/Co-Advisor.

Subjects/Keywords: ultrasound tomography; inverse scattering problem; regularization

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Yun, X. (2019). RECONSTRUCTION OF ULTRASOUND TOMOGRAPHY FOR CANCER DETECTION USING ADVANCED REGULARIZATION METHODS. (Thesis). Penn State University. Retrieved from https://submit-etda.libraries.psu.edu/catalog/16034xuy43

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Yun, Xingzhao. “RECONSTRUCTION OF ULTRASOUND TOMOGRAPHY FOR CANCER DETECTION USING ADVANCED REGULARIZATION METHODS.” 2019. Thesis, Penn State University. Accessed March 01, 2021. https://submit-etda.libraries.psu.edu/catalog/16034xuy43.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Yun, Xingzhao. “RECONSTRUCTION OF ULTRASOUND TOMOGRAPHY FOR CANCER DETECTION USING ADVANCED REGULARIZATION METHODS.” 2019. Web. 01 Mar 2021.

Vancouver:

Yun X. RECONSTRUCTION OF ULTRASOUND TOMOGRAPHY FOR CANCER DETECTION USING ADVANCED REGULARIZATION METHODS. [Internet] [Thesis]. Penn State University; 2019. [cited 2021 Mar 01]. Available from: https://submit-etda.libraries.psu.edu/catalog/16034xuy43.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Yun X. RECONSTRUCTION OF ULTRASOUND TOMOGRAPHY FOR CANCER DETECTION USING ADVANCED REGULARIZATION METHODS. [Thesis]. Penn State University; 2019. Available from: https://submit-etda.libraries.psu.edu/catalog/16034xuy43

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Manchester

12. Perez Alday, Erick Andres. Theoretical investigation of non-invasive methods to identify origins of cardiac arrhythmias.

Degree: PhD, 2016, University of Manchester

URL: https://www.research.manchester.ac.uk/portal/en/theses/theoretical-investigation-of-noninvasive-methods-to-identify-origins-of-cardiac-arrhythmias(2342bbf6-167e-4cd3-a22c-c0cbfd7d8647).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.727908

► Cardiac disease is one of the leading causes of death in the world, with an increase in cardiac arrhythmias in recent years. In addition, myocardial… (more)

Subjects/Keywords: 616.1; Cardiac Arrhythmias; Forward and Inverse problem

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Perez Alday, E. A. (2016). Theoretical investigation of non-invasive methods to identify origins of cardiac arrhythmias. (Doctoral Dissertation). University of Manchester. Retrieved from https://www.research.manchester.ac.uk/portal/en/theses/theoretical-investigation-of-noninvasive-methods-to-identify-origins-of-cardiac-arrhythmias(2342bbf6-167e-4cd3-a22c-c0cbfd7d8647).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.727908

Chicago Manual of Style (16^th Edition):

Perez Alday, Erick Andres. “Theoretical investigation of non-invasive methods to identify origins of cardiac arrhythmias.” 2016. Doctoral Dissertation, University of Manchester. Accessed March 01, 2021. https://www.research.manchester.ac.uk/portal/en/theses/theoretical-investigation-of-noninvasive-methods-to-identify-origins-of-cardiac-arrhythmias(2342bbf6-167e-4cd3-a22c-c0cbfd7d8647).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.727908.

MLA Handbook (7^th Edition):

Perez Alday, Erick Andres. “Theoretical investigation of non-invasive methods to identify origins of cardiac arrhythmias.” 2016. Web. 01 Mar 2021.

Vancouver:

Perez Alday EA. Theoretical investigation of non-invasive methods to identify origins of cardiac arrhythmias. [Internet] [Doctoral dissertation]. University of Manchester; 2016. [cited 2021 Mar 01]. Available from: https://www.research.manchester.ac.uk/portal/en/theses/theoretical-investigation-of-noninvasive-methods-to-identify-origins-of-cardiac-arrhythmias(2342bbf6-167e-4cd3-a22c-c0cbfd7d8647).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.727908.

Council of Science Editors:

Perez Alday EA. Theoretical investigation of non-invasive methods to identify origins of cardiac arrhythmias. [Doctoral Dissertation]. University of Manchester; 2016. Available from: https://www.research.manchester.ac.uk/portal/en/theses/theoretical-investigation-of-noninvasive-methods-to-identify-origins-of-cardiac-arrhythmias(2342bbf6-167e-4cd3-a22c-c0cbfd7d8647).html ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.727908

University of Tennessee – Knoxville

13. Chen, Hongchu. Two-Dimensional Formulation and Quasi-One-Dimensional Approximation to Inverse Heat Conduction by the Calibration Integral Equation Method (CIEM).

Degree: MS, Mechanical Engineering, 2013, University of Tennessee – Knoxville

URL: https://trace.tennessee.edu/utk_gradthes/2401

► The recently devised calibration integral equation method developed at the University of Tennessee for resolving transient inverse heat conduction in one-dimensional applications is extended… (more)

▼ The recently devised calibration integral equation method developed at the University of Tennessee for resolving transient inverse heat conduction in one-dimensional applications is extended and studied in the context of two-dimensional linear inverse heat conduction. This study investigates a simplified plate geometry possessing three known boundary conditions and one unknown boundary condition. This plate contains a series of temperature sensors located on a fixed plane below the surface of interest. To begin the investigation, a quasi-one-dimensional formulation is proposed for predicting the surface heat flux (W/m²) based on a zonal formulation where each zone contains a single thermocouple. In this way, a locally one-dimensional view is proposed for predicting the local or zonal surface heat flux. The thermocouple data set is composed of physically two-dimensional information; however, each surface projection only considers one-dimensional heat flow based on its zone. In this concept, each zone produces a spatial constant heat flux that can temporally vary from zone-to-zone. Each zonal surface heat flux is mathematically described in terms of a Volterra integral equation of the first kind. Being ill posed, regularization based on a local future time method is introduced for stabilization. A new metric is proposed and demonstrated for extracting the optimal regularization parameter. This zonal approximation for materials composed of a low thermal conductivity is shown to yield favorable results. The second study presented in this thesis considers the development of a total heat transfer (W) calibration integral equation based on a fully two-dimensional analysis. In this form, the total surface heat transfer (i.e., the spatially integrated value along the entire surface of interest), is directly derived and implement bypassing the need to determine the local surface heat flux (W/m²). This formulation yields a Volterra integral equation of the first kind similar to the mathematical structure previously described. In many applications, the total surface heat transfer is more important than the local surface heat flux. As such, this new formulation appears highly pertinent. This formulation is shown to produce favorable results over a large range of thermal conductivities and thermal diffusivities. Advisors/Committee Members: Jay I. Frankel, Majid Keyhani, Rao V. Arimilli.

Subjects/Keywords: inverse heat conduction problem; Mechanical Engineering

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Chen, H. (2013). Two-Dimensional Formulation and Quasi-One-Dimensional Approximation to Inverse Heat Conduction by the Calibration Integral Equation Method (CIEM). (Thesis). University of Tennessee – Knoxville. Retrieved from https://trace.tennessee.edu/utk_gradthes/2401

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Chen, Hongchu. “Two-Dimensional Formulation and Quasi-One-Dimensional Approximation to Inverse Heat Conduction by the Calibration Integral Equation Method (CIEM).” 2013. Thesis, University of Tennessee – Knoxville. Accessed March 01, 2021. https://trace.tennessee.edu/utk_gradthes/2401.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Chen, Hongchu. “Two-Dimensional Formulation and Quasi-One-Dimensional Approximation to Inverse Heat Conduction by the Calibration Integral Equation Method (CIEM).” 2013. Web. 01 Mar 2021.

Vancouver:

Chen H. Two-Dimensional Formulation and Quasi-One-Dimensional Approximation to Inverse Heat Conduction by the Calibration Integral Equation Method (CIEM). [Internet] [Thesis]. University of Tennessee – Knoxville; 2013. [cited 2021 Mar 01]. Available from: https://trace.tennessee.edu/utk_gradthes/2401.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Chen H. Two-Dimensional Formulation and Quasi-One-Dimensional Approximation to Inverse Heat Conduction by the Calibration Integral Equation Method (CIEM). [Thesis]. University of Tennessee – Knoxville; 2013. Available from: https://trace.tennessee.edu/utk_gradthes/2401

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Waterloo

14. Maki, Erik. Iterated Function Systems with Place-Dependent Probabilities and the Inverse Problem of Measure Approximation Using Moments.

Degree: 2016, University of Waterloo

URL: http://hdl.handle.net/10012/11017

► The study of iterated function systems has close ties with the subject of fractal-based analysis. One important application is the approximation of a target object… (more)

Subjects/Keywords: Inverse Problem; Invariant Measures; Iterated Function Systems

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APA (6^th Edition):

Maki, E. (2016). Iterated Function Systems with Place-Dependent Probabilities and the Inverse Problem of Measure Approximation Using Moments. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/11017

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Maki, Erik. “Iterated Function Systems with Place-Dependent Probabilities and the Inverse Problem of Measure Approximation Using Moments.” 2016. Thesis, University of Waterloo. Accessed March 01, 2021. http://hdl.handle.net/10012/11017.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Maki, Erik. “Iterated Function Systems with Place-Dependent Probabilities and the Inverse Problem of Measure Approximation Using Moments.” 2016. Web. 01 Mar 2021.

Vancouver:

Maki E. Iterated Function Systems with Place-Dependent Probabilities and the Inverse Problem of Measure Approximation Using Moments. [Internet] [Thesis]. University of Waterloo; 2016. [cited 2021 Mar 01]. Available from: http://hdl.handle.net/10012/11017.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Maki E. Iterated Function Systems with Place-Dependent Probabilities and the Inverse Problem of Measure Approximation Using Moments. [Thesis]. University of Waterloo; 2016. Available from: http://hdl.handle.net/10012/11017

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Manchester

15. Perez Alday, Erick Andres. Theoretical investigation of non-invasive methods to identify origins of cardiac arrhythmias.

Degree: 2016, University of Manchester

URL: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:303466

► Cardiac disease is one of the leading causes of death in the world, with an increase in cardiac arrhythmias in recent years. In addition, myocardial… (more)

Subjects/Keywords: Cardiac Arrhythmias; Forward and Inverse problem

Record Details Similar Records Cite « Share

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Perez Alday, E. A. (2016). Theoretical investigation of non-invasive methods to identify origins of cardiac arrhythmias. (Doctoral Dissertation). University of Manchester. Retrieved from http://www.manchester.ac.uk/escholar/uk-ac-man-scw:303466

Chicago Manual of Style (16^th Edition):

Perez Alday, Erick Andres. “Theoretical investigation of non-invasive methods to identify origins of cardiac arrhythmias.” 2016. Doctoral Dissertation, University of Manchester. Accessed March 01, 2021. http://www.manchester.ac.uk/escholar/uk-ac-man-scw:303466.

MLA Handbook (7^th Edition):

Perez Alday, Erick Andres. “Theoretical investigation of non-invasive methods to identify origins of cardiac arrhythmias.” 2016. Web. 01 Mar 2021.

Vancouver:

Perez Alday EA. Theoretical investigation of non-invasive methods to identify origins of cardiac arrhythmias. [Internet] [Doctoral dissertation]. University of Manchester; 2016. [cited 2021 Mar 01]. Available from: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:303466.

Council of Science Editors:

Perez Alday EA. Theoretical investigation of non-invasive methods to identify origins of cardiac arrhythmias. [Doctoral Dissertation]. University of Manchester; 2016. Available from: http://www.manchester.ac.uk/escholar/uk-ac-man-scw:303466

University of Canterbury

16. Kershaw, Helen Elizabeth. Reconstruction of mechanical properties from surface-based motion data for Digital Image Elasto-Tomography using an implicit surface representation of breast tissue structure.

Degree: PhD, Mechanical Engineering, 2012, University of Canterbury

URL: http://dx.doi.org/10.26021/2081

► There has been great interest in recent times in the use of elastography for the characterization of human tissue. Digital Image Elasto-Tomography is a novel… (more)

▼ There has been great interest in recent times in the use of elastography for the characterization of human tissue. Digital Image Elasto-Tomography is a novel breast cancer pre-screening technique under development at the University of Canterbury, which aims to identify and locate stiff areas within the breast that require further investigation using images of the surface motion alone. A calibrated array of five digital cameras is used to capture surface motion of the breast under harmonic actuation. The forward problem, that is the resulting motion for a given mechanical property distribution, is calculated using the Finite Element Method. The inverse problem is to find the mechanical properties which reproduce the measured surface motion through numerical simulation. A reconstruction algorithm is developed using a shape based description to reduce the number of parameters in the inverse problem. A parallel Genetic Algorithm is developed for parameter optimization. A geometric method termed Fitness Function Analysis is shown to improve the inclusion location optimization problem. The ensemble of solutions generated using the Genetic Algorithm is used to produce an optimal and a credible region for inclusion location. Successful single frequency phantom reconstructions are presented. An effective way of combining information from multi-frequency phantom data by examining the characteristics of the measured surface motion using data quality metrics is developed and used to produce improved reconstructions. Results from numerical simulation datasets and a two inclusion phantom used to test the optimization of multiple and ellipsoidal inclusions indicate that although two inclusions can be successfully reconstructed, the single inclusions assumption may suffice even in irregular, heterogeneous cases. This assumption was used to successfully locate the stiffest inclusion in a phantom containing multiple inclusions of differing stiffness based on three multi-frequency datasets. The methods developed in phantoms are applied to three in vivo cases for both single and multi-frequency data with limited success. This thesis builds on previous work undertaken at the University of Canterbury. The original contributions in this work are as follows. A new reconstruction algorithm combining a genetic algorithm with fitness function analysis is developed. The most realistic tissue mimicking phantoms to date are used. An ellipsoidal shape-based description is presented, and applied to the first multi-inclusion reconstructions in DIET. This work presents the first reconstruction using meshes created directly from data using a meshing algorithm developed by Jonas Biehler. A multi-frequency cost function is developed to produce the first multi-frequency and in vivo reconstructions using DIET data.

Subjects/Keywords: elastography; inverse problem; Digital Image Elasto-Tomography

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Kershaw, H. E. (2012). Reconstruction of mechanical properties from surface-based motion data for Digital Image Elasto-Tomography using an implicit surface representation of breast tissue structure. (Doctoral Dissertation). University of Canterbury. Retrieved from http://dx.doi.org/10.26021/2081

Chicago Manual of Style (16^th Edition):

Kershaw, Helen Elizabeth. “Reconstruction of mechanical properties from surface-based motion data for Digital Image Elasto-Tomography using an implicit surface representation of breast tissue structure.” 2012. Doctoral Dissertation, University of Canterbury. Accessed March 01, 2021. http://dx.doi.org/10.26021/2081.

MLA Handbook (7^th Edition):

Kershaw, Helen Elizabeth. “Reconstruction of mechanical properties from surface-based motion data for Digital Image Elasto-Tomography using an implicit surface representation of breast tissue structure.” 2012. Web. 01 Mar 2021.

Vancouver:

Kershaw HE. Reconstruction of mechanical properties from surface-based motion data for Digital Image Elasto-Tomography using an implicit surface representation of breast tissue structure. [Internet] [Doctoral dissertation]. University of Canterbury; 2012. [cited 2021 Mar 01]. Available from: http://dx.doi.org/10.26021/2081.

Council of Science Editors:

Kershaw HE. Reconstruction of mechanical properties from surface-based motion data for Digital Image Elasto-Tomography using an implicit surface representation of breast tissue structure. [Doctoral Dissertation]. University of Canterbury; 2012. Available from: http://dx.doi.org/10.26021/2081

University of Texas – Austin

17. -1537-7364. Inverse problems in photoacoustic imaging : analysis and computation.

Degree: PhD, Mathematics, 2017, University of Texas – Austin

URL: http://hdl.handle.net/2152/62106

► Inverse problems in photoacoustic imaging (PAT) have been extensively studied in recent years due to their importance in applications. This thesis addresses three important aspects… (more)

Subjects/Keywords: Inverse problem; Photoacoustic tomography; Fast algorithm

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APA (6^th Edition):

-1537-7364. (2017). Inverse problems in photoacoustic imaging : analysis and computation. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/62106

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Chicago Manual of Style (16^th Edition):

-1537-7364. “Inverse problems in photoacoustic imaging : analysis and computation.” 2017. Doctoral Dissertation, University of Texas – Austin. Accessed March 01, 2021. http://hdl.handle.net/2152/62106.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

MLA Handbook (7^th Edition):

-1537-7364. “Inverse problems in photoacoustic imaging : analysis and computation.” 2017. Web. 01 Mar 2021.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Vancouver:

-1537-7364. Inverse problems in photoacoustic imaging : analysis and computation. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2017. [cited 2021 Mar 01]. Available from: http://hdl.handle.net/2152/62106.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Council of Science Editors:

-1537-7364. Inverse problems in photoacoustic imaging : analysis and computation. [Doctoral Dissertation]. University of Texas – Austin; 2017. Available from: http://hdl.handle.net/2152/62106

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

King Abdullah University of Science and Technology

18. Asiri, Sharefa M. An Inverse Source Problem for a One-dimensional Wave Equation: An Observer-Based Approach.

Degree: Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, 2013, King Abdullah University of Science and Technology

URL: http://hdl.handle.net/10754/292839

► Observers are well known in the theory of dynamical systems. They are used to estimate the states of a system from some measurements. However, recently… (more)

Subjects/Keywords: Inverse Problem; Wave Equation; Tikhonov Regularization; Observer

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APA (6^th Edition):

Asiri, S. M. (2013). An Inverse Source Problem for a One-dimensional Wave Equation: An Observer-Based Approach. (Thesis). King Abdullah University of Science and Technology. Retrieved from http://hdl.handle.net/10754/292839

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Asiri, Sharefa M. “An Inverse Source Problem for a One-dimensional Wave Equation: An Observer-Based Approach.” 2013. Thesis, King Abdullah University of Science and Technology. Accessed March 01, 2021. http://hdl.handle.net/10754/292839.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Asiri, Sharefa M. “An Inverse Source Problem for a One-dimensional Wave Equation: An Observer-Based Approach.” 2013. Web. 01 Mar 2021.

Vancouver:

Asiri SM. An Inverse Source Problem for a One-dimensional Wave Equation: An Observer-Based Approach. [Internet] [Thesis]. King Abdullah University of Science and Technology; 2013. [cited 2021 Mar 01]. Available from: http://hdl.handle.net/10754/292839.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Asiri SM. An Inverse Source Problem for a One-dimensional Wave Equation: An Observer-Based Approach. [Thesis]. King Abdullah University of Science and Technology; 2013. Available from: http://hdl.handle.net/10754/292839

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Arizona

19. Holman, Benjamin Robert. Analytical Study and Numerical Solution of the Inverse Source Problem Arising in Thermoacoustic Tomography .

Degree: 2016, University of Arizona

URL: http://hdl.handle.net/10150/612954

► In recent years, revolutionary "hybrid" or "multi-physics" methods of medical imaging have emerged. By combining two or three different types of waves these methods overcome… (more)

▼ In recent years, revolutionary "hybrid" or "multi-physics" methods of medical imaging have emerged. By combining two or three different types of waves these methods overcome limitations of classical tomography techniques and deliver otherwise unavailable, potentially life-saving diagnostic information. Thermoacoustic (and photoacoustic) tomography is the most developed multi-physics imaging modality. Thermo- and photo-acoustic tomography require reconstructing initial acoustic pressure in a body from time series of pressure measured on a surface surrounding the body. For the classical case of free space wave propagation, various reconstruction techniques are well known. However, some novel measurement schemes place the object of interest between reflecting walls that form a de facto resonant cavity. In this case, known methods cannot be used. In chapter 2 we present a fast iterative reconstruction algorithm for measurements made at the walls of a rectangular reverberant cavity with a constant speed of sound. We prove the convergence of the iterations under a certain sufficient condition, and demonstrate the effectiveness and efficiency of the algorithm in numerical simulations. In chapter 3 we consider the more general problem of an arbitrarily shaped resonant cavity with a non constant speed of sound and present the gradual time reversal method for computing solutions to the inverse source problem. It consists in solving back in time on the interval [0, T] the initial/boundary value problem for the wave equation, with the Dirichlet boundary data multiplied by a smooth cutoff function. If T is sufficiently large one obtains a good approximation to the initial pressure; in the limit of large T such an approximation converges (under certain conditions) to the exact solution. Advisors/Committee Members: Kunyansky, Leonid A (advisor), Brio, Moysey (committeemember), Indik, Robert (committeemember), Gillette, Andrew (committeemember), Kunyansky, Leonid A. (committeemember).

Subjects/Keywords: inverse source problem; optoacoustic tomography; thermoacoustic tomography; tomography; wave equation; Applied Mathematics; inverse problem

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Holman, B. R. (2016). Analytical Study and Numerical Solution of the Inverse Source Problem Arising in Thermoacoustic Tomography . (Doctoral Dissertation). University of Arizona. Retrieved from http://hdl.handle.net/10150/612954

Chicago Manual of Style (16^th Edition):

Holman, Benjamin Robert. “Analytical Study and Numerical Solution of the Inverse Source Problem Arising in Thermoacoustic Tomography .” 2016. Doctoral Dissertation, University of Arizona. Accessed March 01, 2021. http://hdl.handle.net/10150/612954.

MLA Handbook (7^th Edition):

Holman, Benjamin Robert. “Analytical Study and Numerical Solution of the Inverse Source Problem Arising in Thermoacoustic Tomography .” 2016. Web. 01 Mar 2021.

Vancouver:

Holman BR. Analytical Study and Numerical Solution of the Inverse Source Problem Arising in Thermoacoustic Tomography . [Internet] [Doctoral dissertation]. University of Arizona; 2016. [cited 2021 Mar 01]. Available from: http://hdl.handle.net/10150/612954.

Council of Science Editors:

Holman BR. Analytical Study and Numerical Solution of the Inverse Source Problem Arising in Thermoacoustic Tomography . [Doctoral Dissertation]. University of Arizona; 2016. Available from: http://hdl.handle.net/10150/612954

20. 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)

Subjects/Keywords: inverse problems; inverse scattering problem; potential scattering; boundary control method

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APA (6^th 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 (16^th 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 (7^th 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

21. Vauthrin, Margaux. Etude de quelques modèles en imagerie photoacoustique : Study of some models in photoacoustic imaging.

Degree: Docteur es, Mathématiques Appliquées, 2017, Grenoble Alpes

URL: http://www.theses.fr/2017GREAM030

►

Cette thèse porte sur l'étude de la méthode d'imagerie photoacoustique, une nouvelle modalité hybride permettant de combiner la haute résolution de l'imagerie par ultrasons et… (more)

▼

Cette thèse porte sur l'étude de la méthode d'imagerie photoacoustique, une nouvelle modalité hybride permettant de combiner la haute résolution de l'imagerie par ultrasons et le contraste de l'imagerie optique. Nous y étudions en particulier le problème inverse associé et sa résolution : il se décompose en l'inversion de l'équation d'ondes et en celle de l'équation de diffusion optique, dont le but est de retrouver les paramètres optiques du milieu. Dans la première partie de cette étude nous développons un modèle permettant de prendre en compte les variations de la vitesse acoustique dans le milieu biologique. En effet, la plupart des méthodes d'inversion supposent une vitesse acoustique constante, ce qui est à l'origine d'erreurs dans les reconstructions. La deuxième partie de la thèse porte sur une étude mathématique du phénomène de limitation de la profondeur de l'imagerie photoacoustique. Nous calculons une estimation de stabilité du problème inverse dans le cas d'un milieu stratifié et nous montrons que la reconstruction se dégrade avec la profondeur. Nous étudions dans la dernière partie le phénomène photoacoustique en présence de nanoparticules métalliques : ces marqueurs permettent d'amplifier par des résonances le signal photoacoustique généré autour d'elles. Elles permettent ainsi une meilleure visibilité des tissus en profondeur. Nous explicitons ici le modèle mathématique de génération du signal photoacoustique, ainsi que la résolution théorique du problème inverse photoacoustique dans ce contexte.

This thesis work is related to photoacoustic imaging techniques which are new multiwave modalities in medical imaging that combine both high resolution of ultrasounds and contrast of optical methods. Weprecisely studied the inverse problem that consists of determining the optical coefficients of biologicaltissues from measurement of acoustic waves generated by the photoacoustic effect. The photoacoustic inverse problem proceeds in two steps.We first retrieve the initial pressure from the measurement of the pressure wave on a part of the boundary of the sample. The first inversion takes then the form of a linear inverse source problem and provides internal data for the optical waves that are more sensitive to the contrast of the absorption and diffusion coefficients. In a second step we recover the optical coefficients from the acquired internal data.The aim of this work is to study the two inversions in different contexts. In the first part, we develop a model that takes into account the variations of the acoustic speed in the medium. Indeed, most of the inversion methods suppose that the acoustic speed is constant, and this assumption can lead to errors in the reconstruction of the optical coefficients. The second part of this work is the derivation of stability estimates for the photoacoustic inverse problem in a layered medium. We prove that the reconstruction is getting worse with depth. This is one of the main drawbacks of the photacoustic method, the imaging depth is limited to a few centimeters. The…

Advisors/Committee Members: Triki, Faouzi (thesis director), Desbat, Laurent (thesis director).

Subjects/Keywords: Photoacoustique; Problème inverse; Vitesse acoustique; Photoacoustic; Inverse problem; Acoustic speed

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Vauthrin, M. (2017). Etude de quelques modèles en imagerie photoacoustique : Study of some models in photoacoustic imaging. (Doctoral Dissertation). Grenoble Alpes. Retrieved from http://www.theses.fr/2017GREAM030

Chicago Manual of Style (16^th Edition):

Vauthrin, Margaux. “Etude de quelques modèles en imagerie photoacoustique : Study of some models in photoacoustic imaging.” 2017. Doctoral Dissertation, Grenoble Alpes. Accessed March 01, 2021. http://www.theses.fr/2017GREAM030.

MLA Handbook (7^th Edition):

Vauthrin, Margaux. “Etude de quelques modèles en imagerie photoacoustique : Study of some models in photoacoustic imaging.” 2017. Web. 01 Mar 2021.

Vancouver:

Vauthrin M. Etude de quelques modèles en imagerie photoacoustique : Study of some models in photoacoustic imaging. [Internet] [Doctoral dissertation]. Grenoble Alpes; 2017. [cited 2021 Mar 01]. Available from: http://www.theses.fr/2017GREAM030.

Council of Science Editors:

Vauthrin M. Etude de quelques modèles en imagerie photoacoustique : Study of some models in photoacoustic imaging. [Doctoral Dissertation]. Grenoble Alpes; 2017. Available from: http://www.theses.fr/2017GREAM030

INP Toulouse

22. Costa, Facundo hernan. Bayesian M/EEG source localization with possible joint skull conductivity estimation : Méthodes bayésiennes pour la localisation des sources M/EEG et estimation de la conductivité du crâne.

Degree: Docteur es, Image, Information et Hypermédia, 2017, INP Toulouse

URL: http://www.theses.fr/2017INPT0016

► Les techniques M/EEG permettent de déterminer les changements de l'activité du cerveau, utiles au diagnostic de pathologies cérébrales, telle que l'épilepsie. Ces techniques consistent à… (more)

▼ Les techniques M/EEG permettent de déterminer les changements de l'activité du cerveau, utiles au diagnostic de pathologies cérébrales, telle que l'épilepsie. Ces techniques consistent à mesurer les potentiels électriques sur le scalp et le champ magnétique autour de la tête. Ces mesures sont reliées à l'activité électrique du cerveau par un modèle linéaire dépendant d'une matrice de mélange liée à un modèle physique. La localisation des sources, ou dipôles, des mesures M/EEG consiste à inverser le modèle physique. Cependant, la non-unicité de la solution (due à la loi fondamentale de physique) et le faible nombre de dipôles rendent le problème inverse mal-posé. Sa résolution requiert une forme de régularisation pour restreindre l'espace de recherche. La littérature compte un nombre important de travaux traitant de ce problème, notamment avec des approches variationnelles. Cette thèse développe des méthodes Bayésiennes pour résoudre des problèmes inverses, avec application au traitement des signaux M/EEG. L'idée principale sous-jacente à ce travail est de contraindre les sources à être parcimonieuses. Cette hypothèse est valide dans plusieurs applications, en particulier pour certaines formes d'épilepsie. Nous développons différents modèles Bayésiens hiérarchiques pour considérer la parcimonie des sources. En théorie, contraindre la parcimonie des sources équivaut à minimiser une fonction de coût pénalisée par la norme l0 de leurs positions. Cependant, la régularisation l0 générant des problèmes NP-complets, l'approximation de cette pseudo-norme par la norme l1 est souvent adoptée. Notre première contribution consiste à combiner les deux normes dans un cadre Bayésien, à l'aide d'une loi a priori Bernoulli-Laplace. Un algorithme Monte Carlo par chaîne de Markov est utilisé pour estimer conjointement les paramètres du modèle et les positions et intensités des sources. La comparaison des résultats, selon plusieurs scenarii, avec ceux obtenus par sLoreta et la régularisation par la norme l1 montre des performances intéressantes, mais au détriment d'un coût de calcul relativement élevé. Notre modèle Bernoulli Laplace résout le problème de localisation des sources pour un instant donné. Cependant, il est admis que l'activité cérébrale a une certaine structure spatio-temporelle. L'exploitation de la dimension temporelle est par conséquent intéressante pour contraindre d'avantage le problème. Notre seconde contribution consiste à formuler un modèle de parcimonie structurée pour exploiter ce phénomène biophysique. Précisément, une distribution Bernoulli-Laplacienne multivariée est proposée comme loi a priori pour les dipôles. Une variable latente est introduite pour traiter la loi a posteriori complexe résultante et un algorithme d'échantillonnage original de type Metropolis Hastings est développé. Les résultats montrent que la technique d'échantillonnage proposée améliore significativement la convergence de la méthode MCMC. Une analyse comparative des résultats a été réalisée entre la méthode proposée, une régularisation par… Advisors/Committee Members: Tourneret, Jean-Yves (thesis director), Batatia, Hadj (thesis director).

Subjects/Keywords: Bayésian; Problème inverse; Localisation des sources; Bayesian; Inverse problem; Source localization

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Costa, F. h. (2017). Bayesian M/EEG source localization with possible joint skull conductivity estimation : Méthodes bayésiennes pour la localisation des sources M/EEG et estimation de la conductivité du crâne. (Doctoral Dissertation). INP Toulouse. Retrieved from http://www.theses.fr/2017INPT0016

Chicago Manual of Style (16^th Edition):

Costa, Facundo hernan. “Bayesian M/EEG source localization with possible joint skull conductivity estimation : Méthodes bayésiennes pour la localisation des sources M/EEG et estimation de la conductivité du crâne.” 2017. Doctoral Dissertation, INP Toulouse. Accessed March 01, 2021. http://www.theses.fr/2017INPT0016.

MLA Handbook (7^th Edition):

Costa, Facundo hernan. “Bayesian M/EEG source localization with possible joint skull conductivity estimation : Méthodes bayésiennes pour la localisation des sources M/EEG et estimation de la conductivité du crâne.” 2017. Web. 01 Mar 2021.

Vancouver:

Costa Fh. Bayesian M/EEG source localization with possible joint skull conductivity estimation : Méthodes bayésiennes pour la localisation des sources M/EEG et estimation de la conductivité du crâne. [Internet] [Doctoral dissertation]. INP Toulouse; 2017. [cited 2021 Mar 01]. Available from: http://www.theses.fr/2017INPT0016.

Council of Science Editors:

Costa Fh. Bayesian M/EEG source localization with possible joint skull conductivity estimation : Méthodes bayésiennes pour la localisation des sources M/EEG et estimation de la conductivité du crâne. [Doctoral Dissertation]. INP Toulouse; 2017. Available from: http://www.theses.fr/2017INPT0016

NSYSU

23. Wang, Tui-En. Direct and Inverse Spectral Problems on Quantum Graphs.

Degree: PhD, Applied Mathematics, 2012, NSYSU

URL: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0730112-120420

► Recently there is a lot of interest in the study of Sturm-Liouville problems on graphs, called quantum graphs. However the study on cyclic quantum graphs… (more)

Subjects/Keywords: quantum graphs; inverse spectral problem; Ambarzumyan problem; spectrum; graphene

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APA (6^th Edition):

Wang, T. (2012). Direct and Inverse Spectral Problems on Quantum Graphs. (Doctoral Dissertation). NSYSU. Retrieved from http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0730112-120420

Chicago Manual of Style (16^th Edition):

Wang, Tui-En. “Direct and Inverse Spectral Problems on Quantum Graphs.” 2012. Doctoral Dissertation, NSYSU. Accessed March 01, 2021. http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0730112-120420.

MLA Handbook (7^th Edition):

Wang, Tui-En. “Direct and Inverse Spectral Problems on Quantum Graphs.” 2012. Web. 01 Mar 2021.

Vancouver:

Wang T. Direct and Inverse Spectral Problems on Quantum Graphs. [Internet] [Doctoral dissertation]. NSYSU; 2012. [cited 2021 Mar 01]. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0730112-120420.

Council of Science Editors:

Wang T. Direct and Inverse Spectral Problems on Quantum Graphs. [Doctoral Dissertation]. NSYSU; 2012. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0730112-120420

Texas A&M University

24. Liu, Xuchen. Continuous Versus Discontinuous Elastic Modulus Distribution in Inverse Problems Based on Finite Element Methods.

Degree: MS, Mechanical Engineering, 2015, Texas A&M University

URL: http://hdl.handle.net/1969.1/155332

► Elasticity imaging, which is also known as Elastography, aims to determine the elastic property distribution of non-homogeneous deformable solids such as soft tissues. This can… (more)

▼ Elasticity imaging, which is also known as Elastography, aims to determine the elastic property distribution of non-homogeneous deformable solids such as soft tissues. This can be done non-destructively using displacement fields measured with medical imaging modalities, such as ultrasound or magnetic resonance imaging. Elasticity imaging can potentially be used to detect tumors based on the stiffness contrast between different materials. This requires the solution of an inverse problem in elasticity. This field has been growing very fast in the past decade. One of the most useful applications of elasticity imaging may be in breast cancer diagnosis, where the tumor could potentially be detected and visualized by its stiffness contrast from its surrounding tissues. In this work the inverse problem will be solved for the shear modulus which is directly related to the Young’s modulus through the Poisson’s ratio. The inverse problem is posed as a constrained optimization problem, where the difference between a computed (predicted) and measured displacement field is minimized. The computed displacement field satisfies the equations of equilibrium. The material is modeled as an isotropic and incompressible material. The present work focuses on assessing the solution of the inverse problem for problem domains defined with a continuous and discontinuous shear modulus distribution. In particular, two problem domains will be considered: 1) a stiff inclusion in a homogeneous background representing a stiff tumor surrounded by soft tissues, 2) a layered ring model representing an arterial wall cross-section. The hypothetical "measured" displacement field for these problem domains will be created by solving the finite element forward problem. Additionally, noise will be added to the displacement field to simulate noisy measured displacement data. According to the results of my thesis work, the potential of the elasticity imaging in the medical field is emerging. The inclusion in problem domain 1, representing a stiffer tumor in a uniform background, can be found and located in the shear modulus reconstructions. Thus, these reconstructed images can potentially be used to detect tumors in the medical field. Advisors/Committee Members: Goenezen, Sevan (advisor), Liang, Hong (committee member), Muliana, Anastasia (committee member).

Subjects/Keywords: Elasticity Imaging; forward problem; inverse problem; shear modulus

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Liu, X. (2015). Continuous Versus Discontinuous Elastic Modulus Distribution in Inverse Problems Based on Finite Element Methods. (Masters Thesis). Texas A&M University. Retrieved from http://hdl.handle.net/1969.1/155332

Chicago Manual of Style (16^th Edition):

Liu, Xuchen. “Continuous Versus Discontinuous Elastic Modulus Distribution in Inverse Problems Based on Finite Element Methods.” 2015. Masters Thesis, Texas A&M University. Accessed March 01, 2021. http://hdl.handle.net/1969.1/155332.

MLA Handbook (7^th Edition):

Liu, Xuchen. “Continuous Versus Discontinuous Elastic Modulus Distribution in Inverse Problems Based on Finite Element Methods.” 2015. Web. 01 Mar 2021.

Vancouver:

Liu X. Continuous Versus Discontinuous Elastic Modulus Distribution in Inverse Problems Based on Finite Element Methods. [Internet] [Masters thesis]. Texas A&M University; 2015. [cited 2021 Mar 01]. Available from: http://hdl.handle.net/1969.1/155332.

Council of Science Editors:

Liu X. Continuous Versus Discontinuous Elastic Modulus Distribution in Inverse Problems Based on Finite Element Methods. [Masters Thesis]. Texas A&M University; 2015. Available from: http://hdl.handle.net/1969.1/155332

Indian Institute of Science

25. Reddy, Annem Narayana. Two Inverse Problems In Linear Elasticity With Applications To Force-Sensing And Mechanical Characterization.

Degree: PhD, Faculty of Engineering, 2013, Indian Institute of Science

URL: http://etd.iisc.ac.in/handle/2005/2075

► Two inverse problems in elasticity are addressed with motivation from cellular biomechanics. The first application is computation of holding forces on a cell during its… (more)

Subjects/Keywords: Elasticity; Inverse Problems; Elasticity - Cauchy's Problem; Elastic Boundary Value Problem; Compliant Grippers; Elasticity - Inverse Problems; Cauchy’s Problem; Inverse Boundary Value Problem; Materials Science

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Reddy, A. N. (2013). Two Inverse Problems In Linear Elasticity With Applications To Force-Sensing And Mechanical Characterization. (Doctoral Dissertation). Indian Institute of Science. Retrieved from http://etd.iisc.ac.in/handle/2005/2075

Chicago Manual of Style (16^th Edition):

Reddy, Annem Narayana. “Two Inverse Problems In Linear Elasticity With Applications To Force-Sensing And Mechanical Characterization.” 2013. Doctoral Dissertation, Indian Institute of Science. Accessed March 01, 2021. http://etd.iisc.ac.in/handle/2005/2075.

MLA Handbook (7^th Edition):

Reddy, Annem Narayana. “Two Inverse Problems In Linear Elasticity With Applications To Force-Sensing And Mechanical Characterization.” 2013. Web. 01 Mar 2021.

Vancouver:

Reddy AN. Two Inverse Problems In Linear Elasticity With Applications To Force-Sensing And Mechanical Characterization. [Internet] [Doctoral dissertation]. Indian Institute of Science; 2013. [cited 2021 Mar 01]. Available from: http://etd.iisc.ac.in/handle/2005/2075.

Council of Science Editors:

Reddy AN. Two Inverse Problems In Linear Elasticity With Applications To Force-Sensing And Mechanical Characterization. [Doctoral Dissertation]. Indian Institute of Science; 2013. Available from: http://etd.iisc.ac.in/handle/2005/2075

University of Texas – Austin

26. -5094-3283. Advanced techniques for multi-source, multi-parameter, and multi-physics inverse problems.

Degree: PhD, Computational Science, Engineering, and Mathematics, 2017, University of Texas – Austin

URL: http://hdl.handle.net/2152/63471

► With the increase in compute power and the advent of the big data era, inverse problems have grown more complex, attempting to extract more information… (more)

Subjects/Keywords: Multi-parameter; Multi-physics; Multi-source; Inverse problem; Joint inverse problem; Vectorial total variation; Primal-dual Newton method; Optimal experimental design; Bayesian inverse problem

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APA (6^th Edition):

-5094-3283. (2017). Advanced techniques for multi-source, multi-parameter, and multi-physics inverse problems. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/63471

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Chicago Manual of Style (16^th Edition):

-5094-3283. “Advanced techniques for multi-source, multi-parameter, and multi-physics inverse problems.” 2017. Doctoral Dissertation, University of Texas – Austin. Accessed March 01, 2021. http://hdl.handle.net/2152/63471.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

MLA Handbook (7^th Edition):

-5094-3283. “Advanced techniques for multi-source, multi-parameter, and multi-physics inverse problems.” 2017. Web. 01 Mar 2021.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Vancouver:

-5094-3283. Advanced techniques for multi-source, multi-parameter, and multi-physics inverse problems. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2017. [cited 2021 Mar 01]. Available from: http://hdl.handle.net/2152/63471.

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

Council of Science Editors:

-5094-3283. Advanced techniques for multi-source, multi-parameter, and multi-physics inverse problems. [Doctoral Dissertation]. University of Texas – Austin; 2017. Available from: http://hdl.handle.net/2152/63471

Note: this citation may be lacking information needed for this citation format:
Author name may be incomplete

27. Nguyen, Manh Tu. Identification multi-échelle du champ d'élasticité apparent stochastique de microstructures hétérogènes : application à un tissu biologique : Multiscale identification of stochastic apparent elasticity field of heterogeneous microstructures : application to a biological tissue.

Degree: Docteur es, Mécanique, 2013, Université Paris-Est

URL: http://www.theses.fr/2013PEST1135

►

Dans le cadre de l'élasticité linéaire 3D des microstructures complexes qui ne peuvent pas être simplement décrites en terme de constituants telles que des tissus… (more)

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Dans le cadre de l'élasticité linéaire 3D des microstructures complexes qui ne peuvent pas être simplement décrites en terme de constituants telles que des tissus biologiques, nous proposons, dans ce travail de recherche, une méthodologie d'identification expérimentale multi-échelle du champ stochastique d'élasticité apparent de la microstructure à l'échelle mésoscopique en utilisant des mesures de champ de déplacements aux échelles macroscopique et mésoscopique. On peut alors utiliser cette méthodologie dans le cadre de changement d'échelle pour obtenir des propriétés mécaniques à l'échelle macroscopique. Dans ce contexte, la question majeure est celle de l'identification expérimentale par résolution d'un problème statistique inverse de la modélisation stochastique introduite pour le champ d'élasticité apparent à l'échelle mésoscopique. Cette identification expérimentale permet non seulement de valider la modélisation mais encore de la rendre utile pour des matériaux existants ayant une microstructure complexe. Le présent travail de recherche est une contribution proposée dans ce cadre pour lequel l'expérimentation et validation expérimentale basée sur des mesures simultanées d'imagerie de champ aux échelles macroscopique et mésoscopique sont faites sur de l'os cortical

In the framework of linear elasticity 3D for complex microstructures that cannot be simply described in terms of components such as biological tissues, we propose, in this research work, a methodology for multiscale experimental identification of the apparent elasticity random field of the microstructure at mesoscopic scale using displacement field measurements at macroscopic scale and mesoscopic scale. We can then use this methodology in the case of changing scale to obtain the mechanical properties at macroscale. In this context, the major issue is the experimental identification by solving a statistical inverse problem of the stochastic modeling introduced for the apparent elasticity random field at mesoscale. This experimental identification allows to validate the modeling and makes it useful for existing materials with complex microstructures. This research work is proposed in this context in which experimentation and experimental validation based on simultaneous measurements of field imaging at macroscale and mesoscale are made on the cortical bonemakes it useful for existing materials with complex microstructures. This research work is proposed in this context in which experimentation and experimental validation based on simultaneous measurements of field imaging at macroscale and mesoscale are made on the cortical bone.

Advisors/Committee Members: Soize, Christian (thesis director).

Subjects/Keywords: Identification multi-échelle; Problème statistique inverse; Modélisation stochastique; Multiscale identification; Statistical inverse problem; Stochastic modeling

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Nguyen, M. T. (2013). Identification multi-échelle du champ d'élasticité apparent stochastique de microstructures hétérogènes : application à un tissu biologique : Multiscale identification of stochastic apparent elasticity field of heterogeneous microstructures : application to a biological tissue. (Doctoral Dissertation). Université Paris-Est. Retrieved from http://www.theses.fr/2013PEST1135

Chicago Manual of Style (16^th Edition):

Nguyen, Manh Tu. “Identification multi-échelle du champ d'élasticité apparent stochastique de microstructures hétérogènes : application à un tissu biologique : Multiscale identification of stochastic apparent elasticity field of heterogeneous microstructures : application to a biological tissue.” 2013. Doctoral Dissertation, Université Paris-Est. Accessed March 01, 2021. http://www.theses.fr/2013PEST1135.

MLA Handbook (7^th Edition):

Nguyen, Manh Tu. “Identification multi-échelle du champ d'élasticité apparent stochastique de microstructures hétérogènes : application à un tissu biologique : Multiscale identification of stochastic apparent elasticity field of heterogeneous microstructures : application to a biological tissue.” 2013. Web. 01 Mar 2021.

Vancouver:

Nguyen MT. Identification multi-échelle du champ d'élasticité apparent stochastique de microstructures hétérogènes : application à un tissu biologique : Multiscale identification of stochastic apparent elasticity field of heterogeneous microstructures : application to a biological tissue. [Internet] [Doctoral dissertation]. Université Paris-Est; 2013. [cited 2021 Mar 01]. Available from: http://www.theses.fr/2013PEST1135.

Council of Science Editors:

Nguyen MT. Identification multi-échelle du champ d'élasticité apparent stochastique de microstructures hétérogènes : application à un tissu biologique : Multiscale identification of stochastic apparent elasticity field of heterogeneous microstructures : application to a biological tissue. [Doctoral Dissertation]. Université Paris-Est; 2013. Available from: http://www.theses.fr/2013PEST1135

28. Zaki, Sabit Fawzi Philippe. Classification par réseaux de neurones dans le cadre de la scattérométrie ellipsométrique : Neural classification in ellipsometric scatterometry.

Degree: Docteur es, Optique, Photonique, Hyperfréquences, 2016, Lyon

URL: http://www.theses.fr/2016LYSES070

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La miniaturisation des composants impose à l’industrie de la micro-électronique de trouver des techniques de caractérisation fiables rapides et si possible à moindre coût. Les… (more)

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La miniaturisation des composants impose à l’industrie de la micro-électronique de trouver des techniques de caractérisation fiables rapides et si possible à moindre coût. Les méthodes optiques telles que la scattérométrie se présentent aujourd’hui comme des alternatives prometteuses répondant à cette problématique de caractérisation. Toutefois, l’ensemble des méthodes scattérométriques nécessitent un certain nombre d’hypothèses pour assurer la résolution d’un problème inverse et notamment la connaissance de la forme géométrique de la structure à tester. Le modèle de structure supposé conditionne la qualité même de la caractérisation. Dans cette thèse, nous proposons l’utilisation des réseaux de neurones comme outils d’aide à la décision en amont de toute méthode de caractérisation. Nous avons validé l’utilisation des réseaux de neurones dans le cadre de la reconnaissance des formes géométriques de l’échantillon à tester par la signature optique utilisée dans toute étape de caractérisation scattérométrique. Tout d’abord, le cas d’un défaut lithographique particulier lié à la présence d’une couche résiduelle de résine au fond des sillons est étudié. Ensuite, nous effectuons une analyse de détection de défaut de modèle utilisé dans la résolution du problème inverse. Enfin nous relatons les résultats obtenus dans le cadre de la sélection de modèles géométriques par réseaux de neurones en amont d’un processus classique de caractérisation scattérométrique. Ce travail de thèse a montré que les réseaux de neurones peuvent bien répondre à la problématique de classification en scattérométrie ellipsométrique et que l’utilisation de ces derniers peut améliorer cette technique optique de caractérisation

The miniaturization of components in the micro-electronics industry involves the need of fast reliable technique of characterization with lower cost. Optical methods such as scatterometry are today promising alternative to this technological need. However, scatterometric method requires a certain number of hypothesis to ensure the resolution of an inverse problem, in particular the knowledge of the geometrical shape of the structure under test. The assumed model of the structure determines the quality of the characterization. In this thesis, we propose the use of neural networks as decision-making tools upstream of any characterization method. We validated the use of neural networks in the context of recognition of the geometrical shapes of the sample under testing by the use of optical signature in any scatterometric characterization process. First, the case of lithographic defect due to the presence of a resist residual layer at the bottom of the grooves is studied. Then, we carry out an analysis of model defect in the inverse problem resolution. Finally, we report results in the context of selection of geometric models by neural networks upstream of a classical scatterometric characterization process. This thesis has demonstrated that neural networks can well answer the problem of classification in ellipsometric…

Advisors/Committee Members: Bayard, Bernard (thesis director).

Subjects/Keywords: Scattérométrie; Ellipsométrie; Classification; Réseaux de neurones; Problème inverse; Scatterometry; Ellipsometry; Classification; Neural networks; Inverse problem

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Zaki, S. F. P. (2016). Classification par réseaux de neurones dans le cadre de la scattérométrie ellipsométrique : Neural classification in ellipsometric scatterometry. (Doctoral Dissertation). Lyon. Retrieved from http://www.theses.fr/2016LYSES070

Chicago Manual of Style (16^th Edition):

Zaki, Sabit Fawzi Philippe. “Classification par réseaux de neurones dans le cadre de la scattérométrie ellipsométrique : Neural classification in ellipsometric scatterometry.” 2016. Doctoral Dissertation, Lyon. Accessed March 01, 2021. http://www.theses.fr/2016LYSES070.

MLA Handbook (7^th Edition):

Zaki, Sabit Fawzi Philippe. “Classification par réseaux de neurones dans le cadre de la scattérométrie ellipsométrique : Neural classification in ellipsometric scatterometry.” 2016. Web. 01 Mar 2021.

Vancouver:

Zaki SFP. Classification par réseaux de neurones dans le cadre de la scattérométrie ellipsométrique : Neural classification in ellipsometric scatterometry. [Internet] [Doctoral dissertation]. Lyon; 2016. [cited 2021 Mar 01]. Available from: http://www.theses.fr/2016LYSES070.

Council of Science Editors:

Zaki SFP. Classification par réseaux de neurones dans le cadre de la scattérométrie ellipsométrique : Neural classification in ellipsometric scatterometry. [Doctoral Dissertation]. Lyon; 2016. Available from: http://www.theses.fr/2016LYSES070

29. Tsou, Chun-Hsiang. Target identification using electroreception : Identification d'une cible par l'électro-localisation.

Degree: Docteur es, Mathématiques Appliquées, 2017, Université Grenoble Alpes (ComUE)

URL: http://www.theses.fr/2017GREAM099

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L’électro-localisation est le nom donné aux capacités sensorielles de certains poissons électriques, vivant en eaux troubles, capables de détecter les perturbations électrostatiques dues à la… (more)

Subjects/Keywords: Problème inverse; Équations de conduction; Électro-Localisation; Inverse problem; Conduction equations; Electroreception; 510

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Tsou, C. (2017). Target identification using electroreception : Identification d'une cible par l'électro-localisation. (Doctoral Dissertation). Université Grenoble Alpes (ComUE). Retrieved from http://www.theses.fr/2017GREAM099

Chicago Manual of Style (16^th Edition):

Tsou, Chun-Hsiang. “Target identification using electroreception : Identification d'une cible par l'électro-localisation.” 2017. Doctoral Dissertation, Université Grenoble Alpes (ComUE). Accessed March 01, 2021. http://www.theses.fr/2017GREAM099.

MLA Handbook (7^th Edition):

Tsou, Chun-Hsiang. “Target identification using electroreception : Identification d'une cible par l'électro-localisation.” 2017. Web. 01 Mar 2021.

Vancouver:

Tsou C. Target identification using electroreception : Identification d'une cible par l'électro-localisation. [Internet] [Doctoral dissertation]. Université Grenoble Alpes (ComUE); 2017. [cited 2021 Mar 01]. Available from: http://www.theses.fr/2017GREAM099.

Council of Science Editors:

Tsou C. Target identification using electroreception : Identification d'une cible par l'électro-localisation. [Doctoral Dissertation]. Université Grenoble Alpes (ComUE); 2017. Available from: http://www.theses.fr/2017GREAM099

30. Hellio, Gabrielle. Modèles stochastiques de mesures archéomagnétiques : Stochastic modeling of archeomagnetic measurements.

Degree: Docteur es, Terre solide, 2015, Université Grenoble Alpes (ComUE)

URL: http://www.theses.fr/2015GREAU004

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Cette thèse porte sur la construction de modèles stochastiques, régionaux et globaux du champ magnétique sur les quatre derniers millénaires à l'aide de mesures archéomagnétiques.… (more)

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Cette thèse porte sur la construction de modèles stochastiques, régionaux et globaux du champ magnétique sur les quatre derniers millénaires à l'aide de mesures archéomagnétiques. Ces données présentent une répartition spatiale et temporelle très inhomogène, et sont caractérisées par de fortes incertitudes sur la mesure et sur la date. La reconstruction du champ constitue alors un problème inverse mal posé. Afin de déterminer la solution la plus adaptée, une information a priori sur le modèle doit être choisie. Elle consiste généralement en une régularisation arbitraire du champ magnétique (lissage en temps et en espace). Contrairement aux études précédentes, nous utilisons les statistiques temporelles du champ magnétique, dérivées des données d'observatoires, satellitaires et paléomagnétiques pour définir l'information a priori via des fonctions d'auto-covariances. Ces statistiques sont confirmées par des résultats issus de simulations numériques. Cette méthode bayésienne permet de s'affranchir de l'utilisation de fonctions supports arbitraires comme les splines pour l'interpolation temporelle. Le résultat final consiste en un ensemble de réalisations possibles du champ magnétique dont la dispersion caractérise l'incertitude sur le modèle. Afin de prendre en compte les erreurs de datation, nous développons par ailleurs une méthode basée sur l'utilisation de Markov Chain Monte Carlo (MCMC). Elle nous permet d'explorer de manière efficace l'espace des dates possibles et ainsi de sélectionner les modèles les plus probables. Cette méthode est une amélioration de la méthode de bootstrap classique, qui donne le même poids à des tirages aléatoires de dates présentant des probabilités très variables. Les ensembles de réalisations sélectionnés par la méthode MCMC aboutissent à la construction d'une densité de probabilités en lieu et place d'une courbe unique. La méthode bayésienne combinée à la méthode Markov Chain Monte Carlo nous a permis de construire des courbes régionales présentant des variations plus rapides que celles obtenues par d'autres études. Les courbes représentées sous forme de densités de probabilités ne sont pas nécessairement gaussiennes, et la méthode permet d'affiner l'estimation de l'âge de chacune des observations. La méthode bayésienne a été utilisée pour la construction de modèles globaux pour lesquels le dipôle axial présente des variations plus rapides que celui obtenu par de précédentes études. D'autre part, le champ magnétique obtenu pour les époques les plus récentes est raisonnablement similaire à celui construit à partir de mesures directes (satellites, observatoires, historiques) malgré des données beaucoup moins nombreuses et une répartition beaucoup moins homogène. Les modèles issus de cette étude offrent une alternative aux modèles existants régularisés, et pourront servir dans un objectif d'assimilation de données avec des modèles de la dynamique dans le noyau terrestre.

The aim of this thesis is to build stochastic models of the magnetic field for the last four millenia from…

Advisors/Committee Members: Jault, Dominique (thesis director), Gillet, Nicolas (thesis director), Bouligand, Claire (thesis director).

Subjects/Keywords: Géomagnétisme; Dynamique du noyau; Problème inverse; Archéomagnétisme; Geomagnetism; Core dynamics; Inverse problem; Archeomagnetism; 550

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Hellio, G. (2015). Modèles stochastiques de mesures archéomagnétiques : Stochastic modeling of archeomagnetic measurements. (Doctoral Dissertation). Université Grenoble Alpes (ComUE). Retrieved from http://www.theses.fr/2015GREAU004

Chicago Manual of Style (16^th Edition):

Hellio, Gabrielle. “Modèles stochastiques de mesures archéomagnétiques : Stochastic modeling of archeomagnetic measurements.” 2015. Doctoral Dissertation, Université Grenoble Alpes (ComUE). Accessed March 01, 2021. http://www.theses.fr/2015GREAU004.

MLA Handbook (7^th Edition):

Hellio, Gabrielle. “Modèles stochastiques de mesures archéomagnétiques : Stochastic modeling of archeomagnetic measurements.” 2015. Web. 01 Mar 2021.

Vancouver:

Hellio G. Modèles stochastiques de mesures archéomagnétiques : Stochastic modeling of archeomagnetic measurements. [Internet] [Doctoral dissertation]. Université Grenoble Alpes (ComUE); 2015. [cited 2021 Mar 01]. Available from: http://www.theses.fr/2015GREAU004.

Council of Science Editors:

Hellio G. Modèles stochastiques de mesures archéomagnétiques : Stochastic modeling of archeomagnetic measurements. [Doctoral Dissertation]. Université Grenoble Alpes (ComUE); 2015. Available from: http://www.theses.fr/2015GREAU004

Open Access Theses and Dissertations