subject:(Sparse approximation)

University of Michigan

1. Brown, Peter. Sparse Approximation Accelerators with Spiking Neural-Networks.

Degree: PhD, Electrical and Computer Engineering, 2020, University of Michigan

URL: http://hdl.handle.net/2027.42/155317

► Today's mobile intelligent devices are often limited more by the energy required for data communication than for data processing. Thus, in addition to their traditional… (more)

▼ Today's mobile intelligent devices are often limited more by the energy required for data communication than for data processing. Thus, in addition to their traditional uses in signal processing, compressed sensing techniques have now found increasing relevance in low power sensing systems. However, basis pursuit denoising (BPDN), the sparse optimization required by such techniques, typically is too computationally intensive to solve directly, so implementations usually resort to greedy pursuit-based methods which approximate the optimization. Locally competitive algorithms (LCAs), a specific class of spiking recurrent neural-networks, can solve BPDN, but efficiently implementing such networks at scale is difficult. This thesis proposes efficient hardware architectures for BPDN accelerators using the LCA spiking neural-network. One such accelerator is a prototype sparse image coder, which achieves unparalleled energy efficiency with custom analog neurons that this work integrates into the digital design flow. At only 48.9 pJ/pixel and 50.1 nJ/encoding, the efficiency of the mixed-signal prototype is double that of an equivalent fully digital architecture. When tasked with encoding images of handwritten digits, the prototype produces sparse codes that are compressed more than 90% while demonstrably preserving features. Next, a prototype compressed sensing radar processor boosts the accuracy of target range and velocity estimations by over 6x compared to conventional processing techniques. Capable of producing over 100,000 estimates per second, the prototype improves throughput by 8x and efficiency by 18times over state-of-the-art. Furthermore, due to a unique form of synaptic weight compression, the prototype architecture is the largest hardware realization of a fully-connected LCA neural-network to date. Advisors/Committee Members: Flynn, Michael (committee member), Cutler, James W (committee member), Lu, Wei (committee member), Zhang, Zhengya (committee member).

Subjects/Keywords: sparse approximation; spiking neural-network; image sparse coding; compressed sensing radar; Electrical Engineering; Engineering

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APA (6^th Edition):

Brown, P. (2020). Sparse Approximation Accelerators with Spiking Neural-Networks. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/155317

Chicago Manual of Style (16^th Edition):

Brown, Peter. “Sparse Approximation Accelerators with Spiking Neural-Networks.” 2020. Doctoral Dissertation, University of Michigan. Accessed February 27, 2021. http://hdl.handle.net/2027.42/155317.

MLA Handbook (7^th Edition):

Brown, Peter. “Sparse Approximation Accelerators with Spiking Neural-Networks.” 2020. Web. 27 Feb 2021.

Vancouver:

Brown P. Sparse Approximation Accelerators with Spiking Neural-Networks. [Internet] [Doctoral dissertation]. University of Michigan; 2020. [cited 2021 Feb 27]. Available from: http://hdl.handle.net/2027.42/155317.

Council of Science Editors:

Brown P. Sparse Approximation Accelerators with Spiking Neural-Networks. [Doctoral Dissertation]. University of Michigan; 2020. Available from: http://hdl.handle.net/2027.42/155317

University of Southern California

2. Das, Abhimanyu. Subset selection algorithms for prediction.

Degree: PhD, Computer Science, 2011, University of Southern California

URL: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/644551/rec/6197

► In this dissertation, we study the subset selection problem for prediction. It deals with choosing the “best” or “most informative” k-subset from a large set… (more)

▼ In this dissertation, we study the subset selection problem for prediction. It deals with choosing the “best” or “most informative” k-subset from a large set of n > k observable variables, to predict the value of a function or another variable of interest that is related to the observable variables. Natural applications of this problem abound in areas as diverse as medicine, social sciences, economics, numerical analysis, signal processing and sensor networks. There are various mathematical formulations for this problem, depending on the characterization of the best subset and of the dependencies between variables. We study two versions: the first version is a stochastic framework for subset selection of random variables using linear regression, and the second is an adversarial framework for estimating aggregate statistics of a function in the presence of metricspace induced spatial constraints. ❧ The goal of this dissertation is to perform an algorithmic analysis of the subset selection problems, characterize natural conditions which make these problems tractable, and explore polynomial-time algorithms with guaranteed optimal or near-optimal solutions. For the stochastic subset selection problem, we explore two broad approaches for designing efficient approximation algorithms. The first approach uses a graph-theoretic framework to characterize the covariance structure of the problem instance, and design efficient algorithms for several classes of covariance graphs. The second approach uses an algebraic framework based on spectral and submodular analysis, to identify conditions under which greedy algorithms can obtain good performance guarantees. ❧ For adversarial subset selection, we provide efficient deterministic and randomized sampling strategies and corresponding prediction functions to approximate some commonly used aggregate statistics. For the deterministic setting, we show an interesting connection with common clustering problems, and obtain constant factor approximation algorithms for predicting the average and maximum statistics. For the randomized setting, we obtain a polynomial-time approximation scheme for the problem of finding the optimal randomized algorithm for choosing a single sample to predict the average statistic. We also solve the interesting special case of estimating the integral of a univariate Lipschitz-continuous function over the [0, 1] interval using one sample, and design an optimal randomized algorithm in this setting. ❧ For several of our subset selection algorithms, we also experimentally validate our theoretical analysis on several real-world data sets. Advisors/Committee Members: Kempe, David (Committee Chair), Teng, Shang-Hua (Committee Member), Sha, Fei (Committee Member), James, Gareth (Committee Member).

Subjects/Keywords: approximation algorithms; machine learning; regression; feature selection; sparse approximation; compressed sensing; submodularity

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APA (6^th Edition):

Das, A. (2011). Subset selection algorithms for prediction. (Doctoral Dissertation). University of Southern California. Retrieved from http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/644551/rec/6197

Chicago Manual of Style (16^th Edition):

Das, Abhimanyu. “Subset selection algorithms for prediction.” 2011. Doctoral Dissertation, University of Southern California. Accessed February 27, 2021. http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/644551/rec/6197.

MLA Handbook (7^th Edition):

Das, Abhimanyu. “Subset selection algorithms for prediction.” 2011. Web. 27 Feb 2021.

Vancouver:

Das A. Subset selection algorithms for prediction. [Internet] [Doctoral dissertation]. University of Southern California; 2011. [cited 2021 Feb 27]. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/644551/rec/6197.

Council of Science Editors:

Das A. Subset selection algorithms for prediction. [Doctoral Dissertation]. University of Southern California; 2011. Available from: http://digitallibrary.usc.edu/cdm/compoundobject/collection/p15799coll127/id/644551/rec/6197

University of Toronto

3. Li, Matthew T.C. The Anchored Separated Representation for High Dimensional Problems.

Degree: 2015, University of Toronto

URL: http://hdl.handle.net/1807/70437

►

Although topics in science and engineering that involve dimensions beyond x-y-z appear obscure, in truth numerous examples abound. For instance, uncertainty quantification requires approximating and… (more)

Subjects/Keywords: Curse of Dimensionality; Function Decomposition; High Dimensional Problems; Sparse Approximation; 0538

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APA (6^th Edition):

Li, M. T. C. (2015). The Anchored Separated Representation for High Dimensional Problems. (Masters Thesis). University of Toronto. Retrieved from http://hdl.handle.net/1807/70437

Chicago Manual of Style (16^th Edition):

Li, Matthew T C. “The Anchored Separated Representation for High Dimensional Problems.” 2015. Masters Thesis, University of Toronto. Accessed February 27, 2021. http://hdl.handle.net/1807/70437.

MLA Handbook (7^th Edition):

Li, Matthew T C. “The Anchored Separated Representation for High Dimensional Problems.” 2015. Web. 27 Feb 2021.

Vancouver:

Li MTC. The Anchored Separated Representation for High Dimensional Problems. [Internet] [Masters thesis]. University of Toronto; 2015. [cited 2021 Feb 27]. Available from: http://hdl.handle.net/1807/70437.

Council of Science Editors:

Li MTC. The Anchored Separated Representation for High Dimensional Problems. [Masters Thesis]. University of Toronto; 2015. Available from: http://hdl.handle.net/1807/70437

Victoria University of Wellington

4. Jin, Wenyu. Spatial Multizone Soundfield Reproduction Design.

Degree: 2015, Victoria University of Wellington

URL: http://hdl.handle.net/10063/4983

► It is desirable for people sharing a physical space to access different multimedia information streams simultaneously. For a good user experience, the interference of the… (more)

▼ It is desirable for people sharing a physical space to access different multimedia information streams simultaneously. For a good user experience, the interference of the different streams should be held to a minimum. This is straightforward for the video component but currently difficult for the audio sound component. Spatial multizone soundfield reproduction, which aims to provide an individual sound environment to each of a set of listeners without the use of physical isolation or headphones, has drawn significant attention of researchers in recent years. The realization of multizone soundfield reproduction is a conceptually challenging problem as currently most of the soundfield reproduction techniques concentrate on a single zone. This thesis considers the theory and design of a multizone soundfield reproduction system using arrays of loudspeakers in given complex environments. We first introduce a novel method for spatial multizone soundfield reproduction based on describing the desired multizone soundfield as an orthogonal expansion of formulated basis functions over the desired reproduction region. This provides the theoretical basis of both 2-D (height invariant) and 3-D soundfield reproduction for this work. We then extend the reproduction of the multizone soundfield over the desired region to reverberant environments, which is based on the identification of the acoustic transfer function (ATF) from the loudspeaker over the desired reproduction region using sparse methods. The simulation results confirm that the method leads to a significantly reduced number of required microphones for an accurate multizone sound reproduction compared with the state of the art, while it also facilitates the reproduction over a wide frequency range. In addition, we focus on the improvements of the proposed multizone reproduction system with regard to practical implementation. The so-called 2.5D multizone oundfield reproduction is considered to accurately reproduce the desired multizone soundfield over a selected 2-D plane at the height approximately level with the listener’s ears using a single array of loudspeakers with 3-D reverberant settings. Then, we propose an adaptive reverberation cancelation method for the multizone soundfield reproduction within the desired region and simplify the prior soundfield measurement process. Simulation results suggest that the proposed method provides a faster convergence rate than the comparative approaches under the same hardware provision. Finally, we conduct the real-world implementation based on the proposed theoretical work. The experimental results show that we can achieve a very noticeable acoustic energy contrast between the signals recorded in the bright zone and the quiet zone, especially for the system implementation with reverberation equalization. Advisors/Committee Members: Kleijn, Bastiaan.

Subjects/Keywords: Spatial Audio; Multizone Soundfield Reproduction; Reverberation Equalization; Sparse Approximation; Adaptive Filtering

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APA (6^th Edition):

Jin, W. (2015). Spatial Multizone Soundfield Reproduction Design. (Doctoral Dissertation). Victoria University of Wellington. Retrieved from http://hdl.handle.net/10063/4983

Chicago Manual of Style (16^th Edition):

Jin, Wenyu. “Spatial Multizone Soundfield Reproduction Design.” 2015. Doctoral Dissertation, Victoria University of Wellington. Accessed February 27, 2021. http://hdl.handle.net/10063/4983.

MLA Handbook (7^th Edition):

Jin, Wenyu. “Spatial Multizone Soundfield Reproduction Design.” 2015. Web. 27 Feb 2021.

Vancouver:

Jin W. Spatial Multizone Soundfield Reproduction Design. [Internet] [Doctoral dissertation]. Victoria University of Wellington; 2015. [cited 2021 Feb 27]. Available from: http://hdl.handle.net/10063/4983.

Council of Science Editors:

Jin W. Spatial Multizone Soundfield Reproduction Design. [Doctoral Dissertation]. Victoria University of Wellington; 2015. Available from: http://hdl.handle.net/10063/4983

University of Florida

5. Xu, Xie. Volumetric Data Reconstruction from Irregular Samples and Compressively Sensed Measurements.

Degree: PhD, Computer Engineering - Computer and Information Science and Engineering, 2014, University of Florida

URL: https://ufdc.ufl.edu/UFE0046527

► Sampling and reconstruction of volumetric data are ubiquitous throughout biomedical imaging, scientific simulation, and visualization applications. In this dissertation, we focus on the reconstruction of… (more)

Subjects/Keywords: Approximation; Boxes; Conceptual lattices; Datasets; Face centered cubic lattices; Interpolation; Mathematical lattices; Sampling rates; Signals; Supernova remnants; box-splines – compressed-sensing – reconstruction – sampling – sparse-approximation – sparse-representation – volumetric-data

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

APA (6^th Edition):

Xu, X. (2014). Volumetric Data Reconstruction from Irregular Samples and Compressively Sensed Measurements. (Doctoral Dissertation). University of Florida. Retrieved from https://ufdc.ufl.edu/UFE0046527

Chicago Manual of Style (16^th Edition):

Xu, Xie. “Volumetric Data Reconstruction from Irregular Samples and Compressively Sensed Measurements.” 2014. Doctoral Dissertation, University of Florida. Accessed February 27, 2021. https://ufdc.ufl.edu/UFE0046527.

MLA Handbook (7^th Edition):

Xu, Xie. “Volumetric Data Reconstruction from Irregular Samples and Compressively Sensed Measurements.” 2014. Web. 27 Feb 2021.

Vancouver:

Xu X. Volumetric Data Reconstruction from Irregular Samples and Compressively Sensed Measurements. [Internet] [Doctoral dissertation]. University of Florida; 2014. [cited 2021 Feb 27]. Available from: https://ufdc.ufl.edu/UFE0046527.

Council of Science Editors:

Xu X. Volumetric Data Reconstruction from Irregular Samples and Compressively Sensed Measurements. [Doctoral Dissertation]. University of Florida; 2014. Available from: https://ufdc.ufl.edu/UFE0046527

Iowa State University

6. Sang, Hejian. Approximate Bayesian approaches and semiparametric methods for handling missing data.

Degree: 2018, Iowa State University

URL: https://lib.dr.iastate.edu/etd/16748

► This thesis consists of four research papers focusing on estimation and inference in missing data. In the first paper (Chapter 2), an approximate Bayesian approach… (more)

Subjects/Keywords: Bayesian approximation computing; Gaussian Mixture Models; Profile likelihood; Sparse model; Statistics and Probability

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APA (6^th Edition):

Sang, H. (2018). Approximate Bayesian approaches and semiparametric methods for handling missing data. (Thesis). Iowa State University. Retrieved from https://lib.dr.iastate.edu/etd/16748

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):

Sang, Hejian. “Approximate Bayesian approaches and semiparametric methods for handling missing data.” 2018. Thesis, Iowa State University. Accessed February 27, 2021. https://lib.dr.iastate.edu/etd/16748.

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

MLA Handbook (7^th Edition):

Sang, Hejian. “Approximate Bayesian approaches and semiparametric methods for handling missing data.” 2018. Web. 27 Feb 2021.

Vancouver:

Sang H. Approximate Bayesian approaches and semiparametric methods for handling missing data. [Internet] [Thesis]. Iowa State University; 2018. [cited 2021 Feb 27]. Available from: https://lib.dr.iastate.edu/etd/16748.

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

Council of Science Editors:

Sang H. Approximate Bayesian approaches and semiparametric methods for handling missing data. [Thesis]. Iowa State University; 2018. Available from: https://lib.dr.iastate.edu/etd/16748

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

Delft University of Technology

7. Varnai, Peter (author). Exploiting Kronecker Structures: With applications to optimization problems arising in the field of adaptive optics.

Degree: 2017, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:98f7cf6e-6ded-4f50-8df7-89944d6a0830

► We study the important mathematical problem of approximating the inverse of low Kronecker-rank matrices in this same form. A traditional alternating least squares (ALS) scheme… (more)

▼ We study the important mathematical problem of approximating the inverse of low Kronecker-rank matrices in this same form. A traditional alternating least squares (ALS) scheme for solving such problems is presented, and we discuss two efficient solutions to the subproblems arising in the corresponding iterations. The first relies on a least-squares formulation while the second on a gradient-based solution from the literature. The former new approach is slightly less efficient but more robust as it does not involve forming the normal equations. We also advocate for employing a Nesterov-type acceleration in the higher level \ac{ALS} scheme. Usage of the resulting algorithm is evaluated in the context of approximating inverses in low Kronecker-rank form in order to preserve this structure for its continued exploitation in applications such as the matrix sign iterations and preconditioning linear systems. Our theoretical study is motivated by two real-life practical applications in the field of adaptive optics (AO). We address each of these in terms of exploiting the Kronecker products featured within their problem formulations. A minimum variance control scheme of wavefront control for atmospheric turbulence correction leads to a large-scale Kronecker structured constrained least-squares problem whose efficient solution is crucial for real-time implementation. Potential approaches based on the alternating direction method of multipliers (ADMM), projected alternating Barzilai-Borwein (PABB), and active sets (AS) methods are analyzed and compared in the context of exploiting the Kronecker structure of the system matrices using data from a partially realistic numerical study. The PABB approach is shown to be the most competitive, also with respective to alternative solutions exploiting only the sparsity of the system matrices instead of their Kronecker form as well. The optimal design of a novel wavefront sensor called a sparse aperture mask (SAM) is also addressed in our work. Here Kronecker products appear when propagating wavefronts using the matrix-form of evaluating two dimensional Fourier transforms. The design problem is formulated in terms of a trade-off between the achievable light throughput of the mask and its ability to distinguish so-called Zernike modes that form a basis for the reconstructed wavefront. Two nonlinear optimization approaches for the solution are presented and discussed in terms of exploiting the Kronecker products by evaluating matrix-vector multiplications with them using a large but sparse philosophy. A final framework is proposed to combine the strengths of these in order to tackle the design problem. Advisors/Committee Members: Verhaegen, Michel (mentor), Sinquin, Baptiste (mentor), Wahls, Sander (graduation committee), Mohajerin Esfahani, Peyman (graduation committee), Delft University of Technology (degree granting institution).

Subjects/Keywords: Kronecker product; inverse approximation; low Kronecker-rank; wavefront control; adaptive optics; sparse aperture mask

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APA (6^th Edition):

Varnai, P. (. (2017). Exploiting Kronecker Structures: With applications to optimization problems arising in the field of adaptive optics. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:98f7cf6e-6ded-4f50-8df7-89944d6a0830

Chicago Manual of Style (16^th Edition):

Varnai, Peter (author). “Exploiting Kronecker Structures: With applications to optimization problems arising in the field of adaptive optics.” 2017. Masters Thesis, Delft University of Technology. Accessed February 27, 2021. http://resolver.tudelft.nl/uuid:98f7cf6e-6ded-4f50-8df7-89944d6a0830.

MLA Handbook (7^th Edition):

Varnai, Peter (author). “Exploiting Kronecker Structures: With applications to optimization problems arising in the field of adaptive optics.” 2017. Web. 27 Feb 2021.

Vancouver:

Varnai P(. Exploiting Kronecker Structures: With applications to optimization problems arising in the field of adaptive optics. [Internet] [Masters thesis]. Delft University of Technology; 2017. [cited 2021 Feb 27]. Available from: http://resolver.tudelft.nl/uuid:98f7cf6e-6ded-4f50-8df7-89944d6a0830.

Council of Science Editors:

Varnai P(. Exploiting Kronecker Structures: With applications to optimization problems arising in the field of adaptive optics. [Masters Thesis]. Delft University of Technology; 2017. Available from: http://resolver.tudelft.nl/uuid:98f7cf6e-6ded-4f50-8df7-89944d6a0830

Louisiana State University

8. Srinivasagopalan, Srivathsan. Oblivious buy-at-bulk network design algorithms.

Degree: PhD, Computer Sciences, 2011, Louisiana State University

URL: etd-04202011-092524 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3439

► Large-scale networks such as the Internet has emerged as arguably the most complex distributed communication network system. The mere size of such networks and all… (more)

▼ Large-scale networks such as the Internet has emerged as arguably the most complex distributed communication network system. The mere size of such networks and all the various applications that run on it brings a large variety of challenging problems. Similar problems lie in any network - transportation, logistics, oil/gas pipeline etc where efficient paths are needed to route the flow of demands. This dissertation studies the computation of efficient paths from the demand sources to their respective destination(s). We consider the buy-at-bulk network design problem in which we wish to compute efficient paths for carrying demands from a set of source nodes to a set of destination nodes. In designing networks, it is important to realize economies of scale. This is can be achieved by aggregating the flow of demands. We want the routing to be oblivious: no matter how many source nodes are there and no matter where they are in the network, the demands from the sources has to be routed in a near-optimal fashion. Moreover, we want the aggregation function f to be unknown, assuming that it is a concave function of the total flow on the edge. The total cost of a solution is determined by the amount of demand routed through each edge. We address questions such as how we can (obliviously) route flows and get competitive algorithms for this problem. We study the approximability of the resulting buy-at-bulk network design problem. Our aim is to _x000C_find minimum-cost paths for all the demands to the sink(s) under two assumptions: (1) The demand set is unknown, that is, the number of source nodes that has demand to send is unknown. (2) The aggregation cost function at intermediate edges is also unknown. We consider di_x000B_fferent types of graphs (doubling-dimension, planar and minor-free) and provide approximate solutions for each of them. For the case of doubling graphs and minor-free graphs, we construct a single spanning tree for the single-source buy-at-bulk network design problem. For the case of planar graphs, we have built a set of paths with an asymptotically tight competitive ratio.

Subjects/Keywords: Spanning Tree; Network Design; Doubling-Dimension; Sparse Covers; Algorithms; Approximation; Graph Theory; Buy-at-Bulk

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APA (6^th Edition):

Srinivasagopalan, S. (2011). Oblivious buy-at-bulk network design algorithms. (Doctoral Dissertation). Louisiana State University. Retrieved from etd-04202011-092524 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3439

Chicago Manual of Style (16^th Edition):

Srinivasagopalan, Srivathsan. “Oblivious buy-at-bulk network design algorithms.” 2011. Doctoral Dissertation, Louisiana State University. Accessed February 27, 2021. etd-04202011-092524 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3439.

MLA Handbook (7^th Edition):

Srinivasagopalan, Srivathsan. “Oblivious buy-at-bulk network design algorithms.” 2011. Web. 27 Feb 2021.

Vancouver:

Srinivasagopalan S. Oblivious buy-at-bulk network design algorithms. [Internet] [Doctoral dissertation]. Louisiana State University; 2011. [cited 2021 Feb 27]. Available from: etd-04202011-092524 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3439.

Council of Science Editors:

Srinivasagopalan S. Oblivious buy-at-bulk network design algorithms. [Doctoral Dissertation]. Louisiana State University; 2011. Available from: etd-04202011-092524 ; https://digitalcommons.lsu.edu/gradschool_dissertations/3439

9. -5189-8939. A Study Of The Mathematics Of Deep Learning.

Degree: PhD, Applied Mathematics & Statistics, 2020, Johns Hopkins University

URL: http://jhir.library.jhu.edu/handle/1774.2/63535

► "Deep Learning"/"Deep Neural Nets" is a technological marvel that is now increasingly deployed at the cutting-edge of artificial intelligence tasks. This ongoing revolution can be… (more)

▼ "Deep Learning"/"Deep Neural Nets" is a technological marvel that is now increasingly deployed at the cutting-edge of artificial intelligence tasks. This ongoing revolution can be said to have been ignited by the iconic 2012 paper from the University of Toronto titled ``ImageNet Classification with Deep Convolutional Neural Networks'' by Alex Krizhevsky, Ilya Sutskever and Geoffrey E. Hinton. This paper showed that deep nets can be used to classify images into meaningful categories with almost human-like accuracies! As of 2020 this approach continues to produce unprecedented performance for an ever widening variety of novel purposes ranging from playing chess to self-driving cars to experimental astrophysics and high-energy physics. But this new found astonishing success of deep neural nets in the last few years has been hinged on an enormous amount of heuristics and it has turned out to be extremely challenging to be mathematically rigorously explainable. In this thesis we take several steps towards building strong theoretical foundations for these new paradigms of deep-learning. Our proofs here can be broadly grouped into three categories, 1. Understanding Neural Function Spaces We show new circuit complexity theorems for deep neural functions over real and Boolean inputs and prove classification theorems about these function spaces which in turn lead to exact algorithms for empirical risk minimization for depth 2 ReLU nets. We also motivate a measure of complexity of neural functions and leverage techniques from polytope geometry to constructively establish the existence of high-complexity neural functions. 2. Understanding Deep Learning Algorithms We give fast iterative stochastic algorithms which can learn near optimal approximations of the true parameters of a \relu gate in the realizable setting. (There are improved versions of this result available in our papers https://arxiv.org/abs/2005.01699 and https://arxiv.org/abs/2005.04211 which are not included in the thesis.) We also establish the first ever (a) mathematical control on the behaviour of noisy gradient descent on a ReLU gate and (b) proofs of convergence of stochastic and deterministic versions of the widely used adaptive gradient deep-learning algorithms, RMSProp and ADAM. This study also includes a first-of-its-kind detailed empirical study of the hyper-parameter values and neural net architectures when these modern algorithms have a significant advantage over classical acceleration based methods. 3. Understanding The Risk Of (Stochastic) Neural Nets We push forward the emergent technology of PAC-Bayesian bounds for the risk of stochastic neural nets to get bounds which are not only empirically smaller than contemporary theories but also demonstrate smaller rates of growth w.r.t increase in width and depth of the net in experimental tests. These critically depend on our novel theorems proving noise resilience of nets. This work also includes an experimental investigation of the geometric properties of the path… Advisors/Committee Members: Maggioni, Mauro (advisor), Younes, Laurent (committee member), Basu, Amitabh (committee member), Sulam , Jeremias (committee member).

Subjects/Keywords: Deep Learning Neural Networks Stochastic Optimization Function Approximation Sparse Coding PAC-Bayes

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APA (6^th Edition):

-5189-8939. (2020). A Study Of The Mathematics Of Deep Learning. (Doctoral Dissertation). Johns Hopkins University. Retrieved from http://jhir.library.jhu.edu/handle/1774.2/63535

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

Chicago Manual of Style (16^th Edition):

-5189-8939. “A Study Of The Mathematics Of Deep Learning.” 2020. Doctoral Dissertation, Johns Hopkins University. Accessed February 27, 2021. http://jhir.library.jhu.edu/handle/1774.2/63535.

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

MLA Handbook (7^th Edition):

-5189-8939. “A Study Of The Mathematics Of Deep Learning.” 2020. Web. 27 Feb 2021.

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

Vancouver:

-5189-8939. A Study Of The Mathematics Of Deep Learning. [Internet] [Doctoral dissertation]. Johns Hopkins University; 2020. [cited 2021 Feb 27]. Available from: http://jhir.library.jhu.edu/handle/1774.2/63535.

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

Council of Science Editors:

-5189-8939. A Study Of The Mathematics Of Deep Learning. [Doctoral Dissertation]. Johns Hopkins University; 2020. Available from: http://jhir.library.jhu.edu/handle/1774.2/63535

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

UCLA

10. Ren, Fengbo. A Scalable VLSI Architecture for Real-Time and Energy-Ecient Sparse Approximation in Compressive Sensing Systems.

Degree: Electrical Engineering, 2014, UCLA

URL: http://www.escholarship.org/uc/item/73p6w2zv

► Digital electronic industry today relies on Nyquist sampling theorem, which requires to double the size (sampling rate) of the signal representation on the Fourier basis… (more)

▼ Digital electronic industry today relies on Nyquist sampling theorem, which requires to double the size (sampling rate) of the signal representation on the Fourier basis to avoid information loss. However, most natural signals have very sparse representations on some other orthogonal (non-Fourier) basis. This mismatch implies a large redundancy in Nyquist-sampled data, making compression a necessity prior to storage or transmission. Recent advances in compressive sensing (CS) theory offer us an alternative data acquisition framework, which can greatly impact power-starved applications such as wireless sensors. CS techniques provide a universal approach to sample compressible signals at a rate significantly below the Nyquist rate with limited information loss. Therefore, CS is a promising technology for realizing configurable, cost-effective, miniaturized, and ultra-low-power data acquisition devices for mobile and wearable applications.However, the digital signal processing of compressively-sampled data involves solving a sparse approximation problem, which requires iterative-searching algorithms that have high computational complexity and require intensive memory access. As a result, existing software solutions are neither energy-efficient nor cost-effective for real-time processing of compressively-sampled data, especially when the processing is to be performed on energy-limited devices. To solve this problem, this dissertation presents a scalable VLSI architecture that can be implemented on field-programmable gate arrays (FPGAs) or system-on-chips (SoCs) to perform dedicated-hardware-driven sparse approximation. A VLSI soft-IP core of the sparse approximation engine is developed in Verilog-HDL, which supports a floating-point data format with 10 design parameters, providing a high dynamic range and the flexibility for application-specific user customizations. Taking advantage of the algorithm-architecture co-design that leverages algorithm reformulations, configurable architectures, and efficient memory mapping schemes, the proposed VLSI architecture features a 100% utilization of the computing resources and is scalable in terms of computation parallelism and memory capability.The hardware emulation of the soft-IP core on a 28-nm Xilinx Kintex-7 FPGA shows that our design achieves the same level of accuracy as the double-precision C program running on an Intel Core i7-4700MQ mobile processor, while providing 47-147x speed-up for ECG signal reconstruction. Furthermore, a 12-237 KS/s 12.8 mW sparse approximation engine chip is realized in a 40-nm CMOS technology for enabling the mobile data aggregation of compressively sampled biomedical signals in CS-based wireless health monitoring systems. The measurement results show that the sparse approximation engine chip operating at the minimum energy point achieves a real-time throughput for reconstructing 61-237 channels of biomedical signals simultaneously with <1% of a mobile device's 2W power budget, which is 14,100x more energy-efficient than the software solver…

Subjects/Keywords: Electrical engineering; Computer engineering; Compressive Sensing; Energy-Efficient Design; Integrated Circuit; Sparse Approximation; VLSI Architecture; Wireless Health

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APA (6^th Edition):

Ren, F. (2014). A Scalable VLSI Architecture for Real-Time and Energy-Ecient Sparse Approximation in Compressive Sensing Systems. (Thesis). UCLA. Retrieved from http://www.escholarship.org/uc/item/73p6w2zv

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):

Ren, Fengbo. “A Scalable VLSI Architecture for Real-Time and Energy-Ecient Sparse Approximation in Compressive Sensing Systems.” 2014. Thesis, UCLA. Accessed February 27, 2021. http://www.escholarship.org/uc/item/73p6w2zv.

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

MLA Handbook (7^th Edition):

Ren, Fengbo. “A Scalable VLSI Architecture for Real-Time and Energy-Ecient Sparse Approximation in Compressive Sensing Systems.” 2014. Web. 27 Feb 2021.

Vancouver:

Ren F. A Scalable VLSI Architecture for Real-Time and Energy-Ecient Sparse Approximation in Compressive Sensing Systems. [Internet] [Thesis]. UCLA; 2014. [cited 2021 Feb 27]. Available from: http://www.escholarship.org/uc/item/73p6w2zv.

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

Council of Science Editors:

Ren F. A Scalable VLSI Architecture for Real-Time and Energy-Ecient Sparse Approximation in Compressive Sensing Systems. [Thesis]. UCLA; 2014. Available from: http://www.escholarship.org/uc/item/73p6w2zv

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

University of Colorado

11. Peng, Ji. Uncertainty Quantification via Sparse Polynomial Chaos Expansion.

Degree: PhD, Mechanical Engineering, 2015, University of Colorado

URL: https://scholar.colorado.edu/mcen_gradetds/112

► Uncertainty quantification (UQ) is an emerging research area that aims to develop methods for accurate predictions of quantities of interest (QoI's) from complex engineering… (more)

▼ Uncertainty quantification (UQ) is an emerging research area that aims to develop methods for accurate predictions of quantities of interest (QoI's) from complex engineering systems, as well as quantitative validation of the associated mathematical models, with presence of random inputs. To perform a comprehensive UQ analysis, polynomial chaos expansion (PCE) is now a commonly used approach in which the QoI is represented in a series of multi-variate polynomials that are orthogonal with respect to the measure of the inputs. Traditional methods for PCE, such as Monte Carlo, stochastic collocation, least-squares regression, are known to suffer from either slow convergence rate or rapid growth of the computational cost (as the number of random inputs increases) in identifying the PCE coefficients. When the PCE coefficients are sparse, i.e., many of them are negligible, it has been shown that compressive sampling is an effective technique to identify the coefficients with smaller number of system simulations. In the context of compressive sampling, this thesis presents new approaches which improve the accuracy of identifying PCE coefficients, and therefore the PCE itself. In detail, a weighted L_1-minimization including a priori information about the PCE coefficients, a bi-fidelity L_1-minimization, a bi-fidelity orthogonal matching pursuit (OMP), and an L_1-minimization including the derivatives of QoI with respect to the random inputs are proposed. Both theoretical analyses and numerical experiments are presented to demonstrate that all the proposed approaches reduce the cost of computing a PCE. % We use various numerical experiments to show that all the proposed approaches improve the accuracy in PCE approximation. For a QoI whose PCE with respect to the measure of the underlying random inputs is not sparse, a polynomial basis design is proposed where, in addition to the coefficients, the basis functions are also learned from the simulation data. The approach has been empirically shown to find the optimal basis which makes the PCE converge more rapidly, and enhances the accuracy of the PCE approximation. Advisors/Committee Members: Alireza Doostan, Daven Henze, Brandon Jones, Kurt Maute, Oleg Vasilyev.

Subjects/Keywords: Basis design; Compressive sampling; Polynomial chaos expansion; Sparse approximation; Uncertainty quantification; Applied Mathematics; Mechanical Engineering; Statistics and Probability

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APA (6^th Edition):

Peng, J. (2015). Uncertainty Quantification via Sparse Polynomial Chaos Expansion. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/mcen_gradetds/112

Chicago Manual of Style (16^th Edition):

Peng, Ji. “Uncertainty Quantification via Sparse Polynomial Chaos Expansion.” 2015. Doctoral Dissertation, University of Colorado. Accessed February 27, 2021. https://scholar.colorado.edu/mcen_gradetds/112.

MLA Handbook (7^th Edition):

Peng, Ji. “Uncertainty Quantification via Sparse Polynomial Chaos Expansion.” 2015. Web. 27 Feb 2021.

Vancouver:

Peng J. Uncertainty Quantification via Sparse Polynomial Chaos Expansion. [Internet] [Doctoral dissertation]. University of Colorado; 2015. [cited 2021 Feb 27]. Available from: https://scholar.colorado.edu/mcen_gradetds/112.

Council of Science Editors:

Peng J. Uncertainty Quantification via Sparse Polynomial Chaos Expansion. [Doctoral Dissertation]. University of Colorado; 2015. Available from: https://scholar.colorado.edu/mcen_gradetds/112

University of Minnesota

12. Razaviyayn, Meisam. Successive convex approximation: analysis and applications.

Degree: PhD, Electrical Engineering, 2014, University of Minnesota

URL: http://hdl.handle.net/11299/163884

► The block coordinate descent (BCD) method is widely used for minimizing a continuous function f of several block variables. At each iteration of this method,… (more)

▼ The block coordinate descent (BCD) method is widely used for minimizing a continuous function f of several block variables. At each iteration of this method, a single block of variables is optimized, while the remaining variables are held fixed. To ensure the convergence of the BCD method, the subproblem of each block variable needs to be solved to its unique global optimal. Unfortunately, this requirement is often too restrictive for many practical scenarios. In this dissertation, we first study an alternative inexact BCD approach which updates the variable blocks by successively minimizing a sequence of approximations of f which are either locally tight upper bounds of f or strictly convex local approximations of f. Different block selection rules are considered such as cyclic (Gauss-Seidel), greedy (Gauss-Southwell), randomized, or even multiple (Parallel) simultaneous blocks. We characterize the convergence conditions and iteration complexity bounds for a fairly wide class of such methods, especially for the cases where the objective functions are either non-differentiable or non-convex. Also the case of existence of a linear constraint is studied briefly using the alternating direction method of multipliers (ADMM) idea. In addition to the deterministic case, the problem of minimizing the expected value of a cost function parameterized by a random variable is also investigated. An inexact sample average approximation (SAA) method, which is developed based on the successive convex approximation idea, is proposed and its convergence is studied. Our analysis unifies and extends the existing convergence results for many classical algorithms such as the BCD method, the difference of convex functions (DC) method, the expectation maximization (EM) algorithm, as well as the classical stochastic (sub-)gradient (SG) method for the nonsmooth nonconvex optimization, all of which are popular for large scale optimization problems involving big data. In the second part of this dissertation, we apply our proposed framework to two practical problems: interference management in wireless networks and the dictionary learning problem for sparse representation. First, the computational complexity of these problems are studied. Then using the successive convex approximation framework, we propose novel algorithms for these practical problems. The proposed algorithms are evaluated through extensive numerical experiments on real data.

Subjects/Keywords: Beamformer Design; Convex Optimization; Heterogeneous Networks; Sparse Dictionary Leaning; Successive Convex Approximation; Successive Upper-bound Minimization

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APA (6^th Edition):

Razaviyayn, M. (2014). Successive convex approximation: analysis and applications. (Doctoral Dissertation). University of Minnesota. Retrieved from http://hdl.handle.net/11299/163884

Chicago Manual of Style (16^th Edition):

Razaviyayn, Meisam. “Successive convex approximation: analysis and applications.” 2014. Doctoral Dissertation, University of Minnesota. Accessed February 27, 2021. http://hdl.handle.net/11299/163884.

MLA Handbook (7^th Edition):

Razaviyayn, Meisam. “Successive convex approximation: analysis and applications.” 2014. Web. 27 Feb 2021.

Vancouver:

Razaviyayn M. Successive convex approximation: analysis and applications. [Internet] [Doctoral dissertation]. University of Minnesota; 2014. [cited 2021 Feb 27]. Available from: http://hdl.handle.net/11299/163884.

Council of Science Editors:

Razaviyayn M. Successive convex approximation: analysis and applications. [Doctoral Dissertation]. University of Minnesota; 2014. Available from: http://hdl.handle.net/11299/163884

University of Melbourne

13. Qadar, Muhammad Ali. Adaptive canonical correlation analysis methods for effective fMRI data analysis.

Degree: 2018, University of Melbourne

URL: http://hdl.handle.net/11343/225001

► Functional magnetic resonance imaging (fMRI) is a powerful non-invasive technique that enables monitoring blood oxygenation level dependent (BOLD) contrasts as a proxy for neuronal activity.… (more)

▼ Functional magnetic resonance imaging (fMRI) is a powerful non-invasive technique that enables monitoring blood oxygenation level dependent (BOLD) contrasts as a proxy for neuronal activity. fMRI data analysis is an emerging field that addresses various problems concerning neuroimaging using fMRI data, including functional connectivity analysis, which entails identifying brain regions associated with certain cognitive tasks as well as investigating the temporal inter-connectivity between brain regions. Functional connectivity networks are usually determined by employing statistical data analysis techniques which are categorized into hypothesis-driven and data-driven methods. Among hypothesis-driven techniques, the most widely used approach is statistical parameter mapping (SPM) which employs the general linear model (GLM). One major limitation of hypothesis-driven techniques is that they require prior knowledge about the form of hemodynamic response function (HRF) and the experimental paradigm. On the other hand, data-driven techniques do not require such specifics, making them effective for activation detection in task-related datasets and functional connectivity analysis in resting-state datasets. In general, conventional data-driven techniques suffer from problems such as computational inefficiency, and poor performance in retrieving spatiotemporal information. To address these problems, the present thesis considers fMRI data decomposition while introducing assumptions such as prior information about the temporal structure, sparseness on the spatial characteristics, and autocorrelation on temporal characteristics of the fMRI data. In this thesis, we develop variants of a special type of data-driven method known as canonical correlation analysis (CCA). The strength of CCA lies in its multivariate nature and ability to analyse multiple datasets simultaneously. However, the majority of conventional CCA methods do not account for the above mentioned characteristics of fMRI data. Our goal in this work is to propose novel CCA algorithms to better estimate spatiotemporal components by introducing assumptions about the underlying structure of the data. For every proposed algorithm, extensive simulation studies using artificially generated data as well as experimental fMRI data are carried out in this thesis. The statistical performance of the proposed algorithms has been thoroughly evaluated on four different fMRI datasets quantitatively and by comparative analysis with existing data-driven techniques. Results have shown that the proposed algorithms outperform the traditional data-driven techniques in retrieving activation maps and temporal signals, leading to overall improvements in activation detection and functional connectivity analysis.

Subjects/Keywords: canonical correlation analysis; functional magnetic resonance imaging; sparse decomposition; basis expansion; regularization; 2DCCA; rank-1 approximation; group analysis

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APA (6^th Edition):

Qadar, M. A. (2018). Adaptive canonical correlation analysis methods for effective fMRI data analysis. (Doctoral Dissertation). University of Melbourne. Retrieved from http://hdl.handle.net/11343/225001

Chicago Manual of Style (16^th Edition):

Qadar, Muhammad Ali. “Adaptive canonical correlation analysis methods for effective fMRI data analysis.” 2018. Doctoral Dissertation, University of Melbourne. Accessed February 27, 2021. http://hdl.handle.net/11343/225001.

MLA Handbook (7^th Edition):

Qadar, Muhammad Ali. “Adaptive canonical correlation analysis methods for effective fMRI data analysis.” 2018. Web. 27 Feb 2021.

Vancouver:

Qadar MA. Adaptive canonical correlation analysis methods for effective fMRI data analysis. [Internet] [Doctoral dissertation]. University of Melbourne; 2018. [cited 2021 Feb 27]. Available from: http://hdl.handle.net/11343/225001.

Council of Science Editors:

Qadar MA. Adaptive canonical correlation analysis methods for effective fMRI data analysis. [Doctoral Dissertation]. University of Melbourne; 2018. Available from: http://hdl.handle.net/11343/225001

14. Fair, Kaitlin Lindsay. A biologically plausible sparse approximation solver on neuromorphic hardware.

Degree: PhD, Electrical and Computer Engineering, 2017, Georgia Tech

URL: http://hdl.handle.net/1853/59782

► We develop a novel design methodology to map the biologically plausible Locally Competitive Algorithm (LCA) to the brain-inspired TrueNorth chip to solve for the sparse… (more)

Subjects/Keywords: Neuromorphic; Bio-inspired; TrueNorth; Sparsity; Sparse approximation

…node dynamics of an LCA system. . . . . . . . . . . . . . . 16 2.9 A sparse approximation… …from an overcomplete dictionary. The sparse approximation problem can be solved using the… …sparse approximation of a signal, where the signal is described as a linear combination of a… …dictionary size. Sparse approximation solvers implemented on low-power hardware offer opportunities… …in real-world embedded systems. An efficient sparse approximation solver implemented on…

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APA (6^th Edition):

Fair, K. L. (2017). A biologically plausible sparse approximation solver on neuromorphic hardware. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/59782

Chicago Manual of Style (16^th Edition):

Fair, Kaitlin Lindsay. “A biologically plausible sparse approximation solver on neuromorphic hardware.” 2017. Doctoral Dissertation, Georgia Tech. Accessed February 27, 2021. http://hdl.handle.net/1853/59782.

MLA Handbook (7^th Edition):

Fair, Kaitlin Lindsay. “A biologically plausible sparse approximation solver on neuromorphic hardware.” 2017. Web. 27 Feb 2021.

Vancouver:

Fair KL. A biologically plausible sparse approximation solver on neuromorphic hardware. [Internet] [Doctoral dissertation]. Georgia Tech; 2017. [cited 2021 Feb 27]. Available from: http://hdl.handle.net/1853/59782.

Council of Science Editors:

Fair KL. A biologically plausible sparse approximation solver on neuromorphic hardware. [Doctoral Dissertation]. Georgia Tech; 2017. Available from: http://hdl.handle.net/1853/59782

15. Jo, Jason. Structured low complexity data mining.

Degree: PhD, Mathematics, 2015, University of Texas – Austin

URL: http://hdl.handle.net/2152/31510

► Due to the rapidly increasing dimensionality of modern datasets many classical approximation algorithms have run into severe computational bottlenecks. This has often been referred to… (more)

▼ Due to the rapidly increasing dimensionality of modern datasets many classical approximation algorithms have run into severe computational bottlenecks. This has often been referred to as the “curse of dimensionality.” To combat this, low complexity priors have been used as they enable us to design efficient approximation algorithms which are capable of scaling up to these modern datasets. Typically the reduction in computational complexity comes at the expense of accuracy. However, the tradeoffs have been relatively advantageous to the computational scientist. This is typically referred to as the “blessings of dimensionality.” Solving large underdetermined systems of linear equations has benefited greatly from the sparsity low complexity prior. A priori, solving a large underdetermined system of linear equations is severely ill-posed. However, using a relatively generic class of sampling matrices, assuming a sparsity prior can yield a well-posed linear system of equations. In particular, various greedy iterative approximation algorithms have been developed which can recover and accurately approximate the k-most significant atoms in our signal. For many engineering applications, the distribution of the top k atoms is not arbitrary and itself has some further structure. In the first half of the thesis we will be concerned with incorporating some a priori designed weights to allow for structured sparse approximation. We provide performance guarantees and numerically demonstrate how the appropriate use of weights can yield a simultaneous reduction in sample complexity and an improvement in approximation accuracy. In the second half of the thesis we will consider the collaborative filtering problem, specifically the task of matrix completion. The matrix completion problem is likewise severely ill-posed but with a low rank prior, the matrix completion problem with high probability admits a unique and robust solution via a cadre of convex optimization solvers. The drawback here is that the solvers enjoy strong theoretical guarantees only in the uniform sampling regime. Building upon recent work on non-uniform matrix completion, we propose a completely expert-free empirical procedure to design optimization parameters in the form of positive weights which allow for the recovery of arbitrarily sampled low rank matrices. We provide theoretical guarantees for these empirically learned weights and present numerical simulations which again show that encoding prior knowledge in the form of weights for optimization problems can again yield a simultaneous reduction in sample complexity and an improvement in approximation accuracy. Advisors/Committee Members: Ward, Rachel A. (advisor), Mueller, Peter (committee member), Hadani, Ronny (committee member), Ren, Kui (committee member), Scott, James (committee member).

Subjects/Keywords: Greedy sparse approximation; Weighted matrix completion

…sparse approximation of dense Power Law Signals using m = 128 measurements. Best viewed in… …enjoy structured sparse approximation guarantees, these methods all suffer from the fact that… …complexity and improvement in approximation accuracy. 3 Chapter 2 Structured Sparse Solutions to… …best s-sparse approximation [1] no such method has been developed for the weighted… …x5B;12] is presented to solve the weighted sparse approximation problem. We emphasize…

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APA (6^th Edition):

Jo, J. (2015). Structured low complexity data mining. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/31510

Chicago Manual of Style (16^th Edition):

Jo, Jason. “Structured low complexity data mining.” 2015. Doctoral Dissertation, University of Texas – Austin. Accessed February 27, 2021. http://hdl.handle.net/2152/31510.

MLA Handbook (7^th Edition):

Jo, Jason. “Structured low complexity data mining.” 2015. Web. 27 Feb 2021.

Vancouver:

Jo J. Structured low complexity data mining. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2015. [cited 2021 Feb 27]. Available from: http://hdl.handle.net/2152/31510.

Council of Science Editors:

Jo J. Structured low complexity data mining. [Doctoral Dissertation]. University of Texas – Austin; 2015. Available from: http://hdl.handle.net/2152/31510

NSYSU

16. Chang, Feng-cheng. Novel Gaussian Integer Sparse Code Multiple Access.

Degree: Master, Communications Engineering, 2016, NSYSU

URL: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0722116-110404

► Sparse code multiple access (SCMA) is proposed for 5th generation mobile networks. Because SCMA has good spectrum efficiency. Each user is assigned a SCMA codebook,… (more)

Subjects/Keywords: Peak to Average Power Ratio; Gaussian Approximation of Interference; Sparse Gaussian Integer Perfect Sequence; Message Passing Algorithm; Codebook Design; SCMA; Multiple User Detector

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APA (6^th Edition):

Chang, F. (2016). Novel Gaussian Integer Sparse Code Multiple Access. (Thesis). NSYSU. Retrieved from http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0722116-110404

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):

Chang, Feng-cheng. “Novel Gaussian Integer Sparse Code Multiple Access.” 2016. Thesis, NSYSU. Accessed February 27, 2021. http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0722116-110404.

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

MLA Handbook (7^th Edition):

Chang, Feng-cheng. “Novel Gaussian Integer Sparse Code Multiple Access.” 2016. Web. 27 Feb 2021.

Vancouver:

Chang F. Novel Gaussian Integer Sparse Code Multiple Access. [Internet] [Thesis]. NSYSU; 2016. [cited 2021 Feb 27]. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0722116-110404.

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

Council of Science Editors:

Chang F. Novel Gaussian Integer Sparse Code Multiple Access. [Thesis]. NSYSU; 2016. Available from: http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0722116-110404

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

17. Ribeiro, Flávio Protásio. Arrays de microfones para medida de campos acústicos.

Degree: PhD, Sistemas Eletrônicos, 2012, University of São Paulo

URL: http://www.teses.usp.br/teses/disponiveis/3/3142/tde-26032012-115753/ ;

►

Imageamento acústico é um problema computacionalmente caro e mal-condicionado, que envolve estimar distribuições de fontes com grandes arranjos de microfones. O método clássico para imageamento… (more)

▼

Imageamento acústico é um problema computacionalmente caro e mal-condicionado, que envolve estimar distribuições de fontes com grandes arranjos de microfones. O método clássico para imageamento acústico utiliza beamforming, e produz a distribuição de fontes de interesse convoluída com a função de espalhamento do arranjo. Esta convolução borra a imagem ideal, significativamente diminuindo sua resolução. Convoluções podem ser evitadas com técnicas de ajuste de covariância, que produzem estimativas de alta resolução. Porém, estas têm sido evitadas devido ao seu alto custo computacional. Nesta tese, admitimos um arranjo bidimensional com geometria separável, e desenvolvemos transformadas rápidas para acelerar imagens acústicas em várias ordens de grandeza. Estas transformadas são genéricas, e podem ser aplicadas para acelerar beamforming, algoritmos de deconvolução e métodos de mínimos quadrados regularizados. Assim, obtemos imagens de alta resolução com algoritmos estado-da-arte, mantendo baixo custo computacional. Mostramos que arranjos separáveis produzem estimativas competitivas com as de geometrias espirais logaritmicas, mas com enormes vantagens computacionais. Finalmente, mostramos como estender este método para incorporar calibração, um modelo para propagação em campo próximo e superfícies focais arbitrárias, abrindo novas possibilidades para imagens acústicas.

Acoustic imaging is a computationally intensive and ill-conditioned inverse problem, which involves estimating high resolution source distributions with large microphone arrays. The classical method for acoustic imaging consists of beamforming, and produces the source distribution of interest convolved with the array point spread function. This convolution smears the image of interest, significantly reducing its effective resolution. Convolutions can be avoided with covariance fitting methods, which have been known to produce robust high-resolution estimates. However, these have been avoided due to prohibitive computational costs. In this thesis, we assume a 2D separable array geometry, and develop fast transforms to accelerate acoustic imaging by several orders of magnitude with respect to previous methods. These transforms are very generic, and can be applied to accelerate beamforming, deconvolution algorithms and regularized least-squares solvers. Thus, one can obtain high-resolution images with state-of-the-art algorithms, while maintaining low computational cost. We show that separable arrays deliver accuracy competitive with multi-arm spiral geometries, while producing huge computational benefits. Finally, we show how to extend this approach with array calibration, a near-field propagation model and arbitrary focal surfaces, opening new and exciting possibilities for acoustic imaging.

Advisors/Committee Members: Nascimento, Vítor Heloiz.

Subjects/Keywords: Acoustic imaging; Aproximação de Kronecker; Array processing; Array processing; Fast transform; Imagens acústicas; Kronecker approximation; Mínimos quadrados regularizados; Reconstrução esparsa; Regularized least squares; Sparse reconstruction; Transformadas rápidas

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APA (6^th Edition):

Ribeiro, F. P. (2012). Arrays de microfones para medida de campos acústicos. (Doctoral Dissertation). University of São Paulo. Retrieved from http://www.teses.usp.br/teses/disponiveis/3/3142/tde-26032012-115753/ ;

Chicago Manual of Style (16^th Edition):

Ribeiro, Flávio Protásio. “Arrays de microfones para medida de campos acústicos.” 2012. Doctoral Dissertation, University of São Paulo. Accessed February 27, 2021. http://www.teses.usp.br/teses/disponiveis/3/3142/tde-26032012-115753/ ;.

MLA Handbook (7^th Edition):

Ribeiro, Flávio Protásio. “Arrays de microfones para medida de campos acústicos.” 2012. Web. 27 Feb 2021.

Vancouver:

Ribeiro FP. Arrays de microfones para medida de campos acústicos. [Internet] [Doctoral dissertation]. University of São Paulo; 2012. [cited 2021 Feb 27]. Available from: http://www.teses.usp.br/teses/disponiveis/3/3142/tde-26032012-115753/ ;.

Council of Science Editors:

Ribeiro FP. Arrays de microfones para medida de campos acústicos. [Doctoral Dissertation]. University of São Paulo; 2012. Available from: http://www.teses.usp.br/teses/disponiveis/3/3142/tde-26032012-115753/ ;

Brno University of Technology

18. Hrbáček, Radek. Využití řídké reprezentace signálu při snímání a rekonstrukci v nukleární magnetické rezonanci: Exploitng sparse signal representations in capturing and recovery of nuclear magnetic resonance data.

Degree: 2019, Brno University of Technology

URL: http://hdl.handle.net/11012/26517

► This thesis deals with the nuclear magnetic resonance field, especially spectroscopy and spectroscopy imaging, sparse signal representation and low-rank approximation approaches. Spectroscopy imaging methods are… (more)

Subjects/Keywords: nukleární magnetická rezonance; spektroskopie; spektroskopické zobrazování; řídká reprezentace signálů; komprimované snímání; aproximace s nízkou hodností; nuclear magnetic resonance; spectroscopy; spectroscopy imaging; sparse signal representation; compressed sensing; low-rank approximation

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APA (6^th Edition):

Hrbáček, R. (2019). Využití řídké reprezentace signálu při snímání a rekonstrukci v nukleární magnetické rezonanci: Exploitng sparse signal representations in capturing and recovery of nuclear magnetic resonance data. (Thesis). Brno University of Technology. Retrieved from http://hdl.handle.net/11012/26517

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):

Hrbáček, Radek. “Využití řídké reprezentace signálu při snímání a rekonstrukci v nukleární magnetické rezonanci: Exploitng sparse signal representations in capturing and recovery of nuclear magnetic resonance data.” 2019. Thesis, Brno University of Technology. Accessed February 27, 2021. http://hdl.handle.net/11012/26517.

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

MLA Handbook (7^th Edition):

Hrbáček, Radek. “Využití řídké reprezentace signálu při snímání a rekonstrukci v nukleární magnetické rezonanci: Exploitng sparse signal representations in capturing and recovery of nuclear magnetic resonance data.” 2019. Web. 27 Feb 2021.

Vancouver:

Hrbáček R. Využití řídké reprezentace signálu při snímání a rekonstrukci v nukleární magnetické rezonanci: Exploitng sparse signal representations in capturing and recovery of nuclear magnetic resonance data. [Internet] [Thesis]. Brno University of Technology; 2019. [cited 2021 Feb 27]. Available from: http://hdl.handle.net/11012/26517.

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

Council of Science Editors:

Hrbáček R. Využití řídké reprezentace signálu při snímání a rekonstrukci v nukleární magnetické rezonanci: Exploitng sparse signal representations in capturing and recovery of nuclear magnetic resonance data. [Thesis]. Brno University of Technology; 2019. Available from: http://hdl.handle.net/11012/26517

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

Georgia Tech

19. Shapero, Samuel Andre. Configurable analog hardware for neuromorphic Bayesian inference and least-squares solutions.

Degree: PhD, Electrical and Computer Engineering, 2013, Georgia Tech

URL: http://hdl.handle.net/1853/51719

► Sparse approximation is a Bayesian inference program with a wide number of signal processing applications, such as Compressed Sensing recovery used in medical imaging. Previous… (more)

Subjects/Keywords: Regularized least-squares; Sparse approximation; Analog circuits; FPAA; Neural network; Hopfield network; Locally competitive algorithm (LCA); Least squares; Bayesian statistical decision theory; Analog computers

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

APA (6^th Edition):

Shapero, S. A. (2013). Configurable analog hardware for neuromorphic Bayesian inference and least-squares solutions. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/51719

Chicago Manual of Style (16^th Edition):

Shapero, Samuel Andre. “Configurable analog hardware for neuromorphic Bayesian inference and least-squares solutions.” 2013. Doctoral Dissertation, Georgia Tech. Accessed February 27, 2021. http://hdl.handle.net/1853/51719.

MLA Handbook (7^th Edition):

Shapero, Samuel Andre. “Configurable analog hardware for neuromorphic Bayesian inference and least-squares solutions.” 2013. Web. 27 Feb 2021.

Vancouver:

Shapero SA. Configurable analog hardware for neuromorphic Bayesian inference and least-squares solutions. [Internet] [Doctoral dissertation]. Georgia Tech; 2013. [cited 2021 Feb 27]. Available from: http://hdl.handle.net/1853/51719.

Council of Science Editors:

Shapero SA. Configurable analog hardware for neuromorphic Bayesian inference and least-squares solutions. [Doctoral Dissertation]. Georgia Tech; 2013. Available from: http://hdl.handle.net/1853/51719

University of Edinburgh

20. Yaghoobi Vaighan, Mehrdad. Adaptive sparse coding and dictionary selection.

Degree: PhD, 2010, University of Edinburgh

URL: http://hdl.handle.net/1842/4070

► The sparse coding is approximation/representation of signals with the minimum number of coefficients using an overcomplete set of elementary functions. This kind of approximations/ representations… (more)

▼ The sparse coding is approximation/representation of signals with the minimum number of coefficients using an overcomplete set of elementary functions. This kind of approximations/ representations has found numerous applications in source separation, denoising, coding and compressed sensing. The adaptation of the sparse approximation framework to the coding problem of signals is investigated in this thesis. Open problems are the selection of appropriate models and their orders, coefficient quantization and sparse approximation method. Some of these questions are addressed in this thesis and novel methods developed. Because almost all recent communication and storage systems are digital, an easy method to compute quantized sparse approximations is introduced in the first part. The model selection problem is investigated next. The linear model can be adapted to better fit a given signal class. It can also be designed based on some a priori information about the model. Two novel dictionary selection methods are separately presented in the second part of the thesis. The proposed model adaption algorithm, called Dictionary Learning with the Majorization Method (DLMM), is much more general than current methods. This generality allowes it to be used with different constraints on the model. Particularly, two important cases have been considered in this thesis for the first time, Parsimonious Dictionary Learning (PDL) and Compressible Dictionary Learning (CDL). When the generative model order is not given, PDL not only adapts the dictionary to the given class of signals, but also reduces the model order redundancies. When a fast dictionary is needed, the CDL framework helps us to find a dictionary which is adapted to the given signal class without increasing the computation cost so much. Sometimes a priori information about the linear generative model is given in format of a parametric function. Parametric Dictionary Design (PDD) generates a suitable dictionary for sparse coding using the parametric function. Basically PDD finds a parametric dictionary with a minimal dictionary coherence, which has been shown to be suitable for sparse approximation and exact sparse recovery. Theoretical analyzes are accompanied by experiments to validate the analyzes. This research was primarily used for audio applications, as audio can be shown to have sparse structures. Therefore, most of the experiments are done using audio signals.

Subjects/Keywords: 621.382; sparse approximation; dictionary learning; inverse problems; dictionary design; gradient based optimization

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APA (6^th Edition):

Yaghoobi Vaighan, M. (2010). Adaptive sparse coding and dictionary selection. (Doctoral Dissertation). University of Edinburgh. Retrieved from http://hdl.handle.net/1842/4070

Chicago Manual of Style (16^th Edition):

Yaghoobi Vaighan, Mehrdad. “Adaptive sparse coding and dictionary selection.” 2010. Doctoral Dissertation, University of Edinburgh. Accessed February 27, 2021. http://hdl.handle.net/1842/4070.

MLA Handbook (7^th Edition):

Yaghoobi Vaighan, Mehrdad. “Adaptive sparse coding and dictionary selection.” 2010. Web. 27 Feb 2021.

Vancouver:

Yaghoobi Vaighan M. Adaptive sparse coding and dictionary selection. [Internet] [Doctoral dissertation]. University of Edinburgh; 2010. [cited 2021 Feb 27]. Available from: http://hdl.handle.net/1842/4070.

Council of Science Editors:

Yaghoobi Vaighan M. Adaptive sparse coding and dictionary selection. [Doctoral Dissertation]. University of Edinburgh; 2010. Available from: http://hdl.handle.net/1842/4070

University of South Carolina

21. Savu, Daniel. Sparse Approximation In Banach Spaces.

Degree: PhD, Mathematics, 2009, University of South Carolina

URL: https://scholarcommons.sc.edu/etd/90

► The sparse approximation problems ask for complete recovery of functions in a given space that are supported by few of the elements of a… (more)

▼ The sparse approximation problems ask for complete recovery of functions in a given space that are supported by few of the elements of a system of generators for the space or for approximate recovery that involves a limited number of generators. Traditionally, these problems have been studied by approximation theorists in the context of methods of finding the best approximant from a subspace, or by statisticians concerned in finding good regressions. Recently, a new field of applied mathematics, Compressive Sensing, emerged. It gathered mathematicians, statisticians, electrical engineers, computer scientists, chemists and physicists fascinated by the potential of new algorithms in solving the problem of sparse approximation in diverse settings, which is the primary objective of this field. One of the most successful approaches in this area, the greedy method, belongs to the theory of nonlinear approximation. The greedy algorithms are designed to make local optimal choices with the hope of obtaining a global optimal solution. This is made in regard with redundant systems which offer convenience of representation as well as better rates of approximation. The redundancy raises, in turn, very difficult theoretical problems. This dissertation gives answers to some of these problems in the very general setting of Banach spaces. Its theoretical results complete the previous findings in this setting and show, for the first time, the same general recovery properties as the ones known in the particular case of Hilbert spaces. Moreover, this work provides a novel idea of improvement of the geometry of the redundant systems by switching to a different setting than the standard Hilbert space. This improvement would translate in better recovery properties as the dissertation proved the same efficiency of the greedy approach in the new setting. This investigation finds its place in the fresh area of Compressive Sensing by proposing a competitive alternative in solving sparse approximation problems, and it gives new insights in the Theory of Greedy Approximation. Advisors/Committee Members: Vladimir N. Temlyakov.

Subjects/Keywords: Mathematics; Physical Sciences and Mathematics; Approximation; Banach; Compressive; Greedy; Lebesgue-type; Sparse

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

APA (6^th Edition):

Savu, D. (2009). Sparse Approximation In Banach Spaces. (Doctoral Dissertation). University of South Carolina. Retrieved from https://scholarcommons.sc.edu/etd/90

Chicago Manual of Style (16^th Edition):

Savu, Daniel. “Sparse Approximation In Banach Spaces.” 2009. Doctoral Dissertation, University of South Carolina. Accessed February 27, 2021. https://scholarcommons.sc.edu/etd/90.

MLA Handbook (7^th Edition):

Savu, Daniel. “Sparse Approximation In Banach Spaces.” 2009. Web. 27 Feb 2021.

Vancouver:

Savu D. Sparse Approximation In Banach Spaces. [Internet] [Doctoral dissertation]. University of South Carolina; 2009. [cited 2021 Feb 27]. Available from: https://scholarcommons.sc.edu/etd/90.

Council of Science Editors:

Savu D. Sparse Approximation In Banach Spaces. [Doctoral Dissertation]. University of South Carolina; 2009. Available from: https://scholarcommons.sc.edu/etd/90

University of South Carolina

22. Zheltov, Pavel. Additive Lebesgue-Type Inequalities for Greedy Approximation.

Degree: PhD, Mathematics, 2010, University of South Carolina

URL: https://scholarcommons.sc.edu/etd/430

► In the approximation theory we are commonly interested in finding a best possible approximant to a function (also thought of as a signal or… (more)

Subjects/Keywords: Mathematics; Physical Sciences and Mathematics; algorithms; approximation; compressed; greedy; sensing; sparse

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

APA (6^th Edition):

Zheltov, P. (2010). Additive Lebesgue-Type Inequalities for Greedy Approximation. (Doctoral Dissertation). University of South Carolina. Retrieved from https://scholarcommons.sc.edu/etd/430

Chicago Manual of Style (16^th Edition):

Zheltov, Pavel. “Additive Lebesgue-Type Inequalities for Greedy Approximation.” 2010. Doctoral Dissertation, University of South Carolina. Accessed February 27, 2021. https://scholarcommons.sc.edu/etd/430.

MLA Handbook (7^th Edition):

Zheltov, Pavel. “Additive Lebesgue-Type Inequalities for Greedy Approximation.” 2010. Web. 27 Feb 2021.

Vancouver:

Zheltov P. Additive Lebesgue-Type Inequalities for Greedy Approximation. [Internet] [Doctoral dissertation]. University of South Carolina; 2010. [cited 2021 Feb 27]. Available from: https://scholarcommons.sc.edu/etd/430.

Council of Science Editors:

Zheltov P. Additive Lebesgue-Type Inequalities for Greedy Approximation. [Doctoral Dissertation]. University of South Carolina; 2010. Available from: https://scholarcommons.sc.edu/etd/430

The Ohio State University

23. Zheng, Zizhan. Sparse Deployment of Large Scale Wireless Networks for Mobile Targets.

Degree: PhD, Computer Science and Engineering, 2010, The Ohio State University

URL: http://rave.ohiolink.edu/etdc/view?acc_num=osu1275444923

► Deploying wireless networks at large scale is challenging. Despitevarious effort made in the design of coverage schemes and deploymentalgorithms with static targets in mind,… (more)

▼ Deploying wireless networks at large scale is challenging. Despitevarious effort made in the design of coverage schemes and deploymentalgorithms with static targets in mind, how to deploy awireless network to achieve a desired quality of service for mobile targets moving in a large region without incurringprohibitive cost largely remains open. To address this issue, thisdissertation proposes Sparse Coverage, a deployment scheme thatprovides guaranteed service to mobile targets while trading offservice quality with cost in a deterministic way. The first part of this dissertation discusses two sparse coveragemodels for deploying WiFi access points (APs) along a city-wide roadnetwork to provide data service to mobile vehicles. The first model,called Alpha Coverage, ensures that a vehicle moving through a pathof length α is guaranteed to have a contact with some AP.This is the first partial coverage model (in contrast to the moreexpensive full coverage model) that provides a performance guaranteeto disconnection-tolerant mobile users. We show that under thisgeneral definition, even to verify whether a given deploymentprovides Alpha Coverage is co-NPC. Thus, we propose two practicalmetrics as approximations, and design efficient approximationalgorithms for each of them. The concept of Alpha Coverage is thenextended by taking connectivity into account. To characterize theperformance of a roadside WiFi network more accurately, we proposethe second sparse coverage model, called Contact Opportunity, whichmeasures the fraction of distance or time that a mobile user is incontact with some AP. We present an efficient deployment method thatmaximizes the worst-case contact opportunity under a budgetconstraint by exploiting submodular optimization techniques. Wefurther extend this notion to the more intuitive metric – averagethroughput – by taking various uncertainties involved in the systeminto account. The second part of this dissertation studies sparse deploymenttechniques for placing sensor nodes in a large 2-d region fortracking movements. We propose a sparse coverage model called TrapCoverage, which provides a bound on the largest gap that a mobiletarget, e.g., an intruder or a dynamic event, is missed by anysensor node. In contrast to the current probabilistic partialcoverage models, this is the first 2-d coverage model that can tradeoff the quality of tracking with network lifetime in a deterministicway. For an arbitrarily deployed sensor network, we proposeefficient algorithms for determining the level of TrapCoverage even if the sensing regions have non-convex or uncertainboundaries. We then discuss a roadmap assisted geographic routingprotocol to support efficient pairwise routing in large sensornetworks with holes, which embodies a novel hole approximationtechnique and makes desired tradeoff between route-stretch andcontrol overhead. Advisors/Committee Members: Sinha, Prasun (Advisor).

Subjects/Keywords: Computer Science; Wireless networks; sensor networks; coverage; sparse coverage; approximation algorithms

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APA (6^th Edition):

Zheng, Z. (2010). Sparse Deployment of Large Scale Wireless Networks for Mobile Targets. (Doctoral Dissertation). The Ohio State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=osu1275444923

Chicago Manual of Style (16^th Edition):

Zheng, Zizhan. “Sparse Deployment of Large Scale Wireless Networks for Mobile Targets.” 2010. Doctoral Dissertation, The Ohio State University. Accessed February 27, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=osu1275444923.

MLA Handbook (7^th Edition):

Zheng, Zizhan. “Sparse Deployment of Large Scale Wireless Networks for Mobile Targets.” 2010. Web. 27 Feb 2021.

Vancouver:

Zheng Z. Sparse Deployment of Large Scale Wireless Networks for Mobile Targets. [Internet] [Doctoral dissertation]. The Ohio State University; 2010. [cited 2021 Feb 27]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1275444923.

Council of Science Editors:

Zheng Z. Sparse Deployment of Large Scale Wireless Networks for Mobile Targets. [Doctoral Dissertation]. The Ohio State University; 2010. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1275444923

24. Hu, K. (author). Compressive Sensing for Near-field Source Localization.

Degree: 2014, Delft University of Technology

URL: http://resolver.tudelft.nl/uuid:f0e70c18-52d1-4c9b-a611-dbd534a0190c

►

Near-field source localization is an important aspect in many diverse areas such as acoustics, seismology, to list a few. The planar wave assumption frequently used… (more)

Subjects/Keywords: Near-field source localization; compressive sensing; Fresnel approximation; correlation; sparse modeling; joint sparse recovery; EIV model

…the Fresnel approximation). Chapter 4: Sparse recovery techniques for near-field source… …sparse regression with or without Fresnel approximation for a single snapshot incurs the same… …sparse recovery . . . . . . . 5 5 5 6 7 3 Signal Model 3.1 Spherical wavefront model… …3.2 Fresnel approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 11 12 4… …Sparse recovery techniques for near-field source localization: based model 4.1 Grid-based model…

13 more images…

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APA (6^th Edition):

Hu, K. (. (2014). Compressive Sensing for Near-field Source Localization. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:f0e70c18-52d1-4c9b-a611-dbd534a0190c

Chicago Manual of Style (16^th Edition):

Hu, K (author). “Compressive Sensing for Near-field Source Localization.” 2014. Masters Thesis, Delft University of Technology. Accessed February 27, 2021. http://resolver.tudelft.nl/uuid:f0e70c18-52d1-4c9b-a611-dbd534a0190c.

MLA Handbook (7^th Edition):

Hu, K (author). “Compressive Sensing for Near-field Source Localization.” 2014. Web. 27 Feb 2021.

Vancouver:

Hu K(. Compressive Sensing for Near-field Source Localization. [Internet] [Masters thesis]. Delft University of Technology; 2014. [cited 2021 Feb 27]. Available from: http://resolver.tudelft.nl/uuid:f0e70c18-52d1-4c9b-a611-dbd534a0190c.

Council of Science Editors:

Hu K(. Compressive Sensing for Near-field Source Localization. [Masters Thesis]. Delft University of Technology; 2014. Available from: http://resolver.tudelft.nl/uuid:f0e70c18-52d1-4c9b-a611-dbd534a0190c

25. Spencer, Timothy Scott. Weighted inequalities via dyadic operators and a learning theory approach to compressive sensing.

Degree: PhD, Mathematics, 2017, Georgia Tech

URL: http://hdl.handle.net/1853/58730

► The first part of this dissertation explores the application of dominating operators in harmonic analysis by sparse operators. We present preliminary results on dominating certain… (more)

Subjects/Keywords: Weighted inequalities; Sparse operators; Sparse approximation; 1-bit sensing; Restricted isometry property; Quasi-isometry; Noisy embeddings

…application of dominating operators in harmonic analysis by sparse operators. In the second chapter… …we introduce sparse operators. Presented therein are preliminary results on dominating… …certain operators by sparse operators, and we also prove several analogous results for other… …operators. We make use of the sparse domination introduced in Chapter 2 to derive weighted… …domination by sparse operators, but continues the study of fractional integral operators. There is…

1 more image…

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APA (6^th Edition):

Spencer, T. S. (2017). Weighted inequalities via dyadic operators and a learning theory approach to compressive sensing. (Doctoral Dissertation). Georgia Tech. Retrieved from http://hdl.handle.net/1853/58730

Chicago Manual of Style (16^th Edition):

Spencer, Timothy Scott. “Weighted inequalities via dyadic operators and a learning theory approach to compressive sensing.” 2017. Doctoral Dissertation, Georgia Tech. Accessed February 27, 2021. http://hdl.handle.net/1853/58730.

MLA Handbook (7^th Edition):

Spencer, Timothy Scott. “Weighted inequalities via dyadic operators and a learning theory approach to compressive sensing.” 2017. Web. 27 Feb 2021.

Vancouver:

Spencer TS. Weighted inequalities via dyadic operators and a learning theory approach to compressive sensing. [Internet] [Doctoral dissertation]. Georgia Tech; 2017. [cited 2021 Feb 27]. Available from: http://hdl.handle.net/1853/58730.

Council of Science Editors:

Spencer TS. Weighted inequalities via dyadic operators and a learning theory approach to compressive sensing. [Doctoral Dissertation]. Georgia Tech; 2017. Available from: http://hdl.handle.net/1853/58730

University of Michigan

26. Maleh, Ray. Efficient Sparse Approximation Methods for Medical Imaging.

Degree: PhD, Applied and Interdisciplinary Mathematics, 2009, University of Michigan

URL: http://hdl.handle.net/2027.42/64764

► For thousands of years, doctors had to face the daunting task of diagnosing and treating all sorts of medical ailments without the ability to view… (more)

▼ For thousands of years, doctors had to face the daunting task of diagnosing and treating all sorts of medical ailments without the ability to view the insides of their patients. It was not until the 1970's that CT and MRI technology enabled doctors to develop cross-sectional images of internal anatomy. This work discusses the application of sparse approximation theory and the closely related field compressive sensing to medical image processing. We discuss one related theoretical problem and two major practical applications. Orthogonal Matching Pursuit (OMP) is a fast and efficient greedy algorithm that is well known in the sparse approximation community. We prove restricted isometry conditions that guarantee its correctness and establish theoretical error bounds on its performance. Then we prove stronger results for variations of this algorithm where multiple items are allowed to be selected per iteration. The orthogonalized matching pursuit algorithms are then applied to the problem of recovering sparse gradient images from a small number of Fourier samples. In MRI, this translates into reducing patient scan time by eliminating the need to sample the entire spectrum of an image at the Nyquist rate. A novel algorithm called Gradient Matching Pursuit is introduced that uses some variation of OMP to recover an image in the edge domain and then use one of several proposed inverse-filtering techniques to obtain a final reconstruction. Gradient Matching Pursuit is analyzed theoretically and is empirically shown to perform as accurately, but more efficiently, than conventional total-variation minimization routines. The last part of this work will describe how sparse approximation methods can be utilized to correct imperfections in MRI transmission coils. In the general case of an MRI scanner with multiple transmission coils, the MRI Parallel Excitation problem can be recast into a parallel sparse approximation problem, which is basically an interpolation between sparse and simultaneous sparse approximation. An efficient algorithm called Parallel Orthogonal Matching Pursuit is proposed to solve the MRI Parallel Excitation Problem as well as other similar problems. Advisors/Committee Members: Fessler, Jeffrey A. (committee member), Gilbert, Anna Catherine (committee member), Esedoglu, Selim (committee member), Strauss, Martin (committee member).

Subjects/Keywords: Medical Imaging; Sparse Approximation; Compressive Sensing; Parallel Approximation; Matching Pursuit; Parallel Excitation; Engineering; Health Sciences; Science

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APA (6^th Edition):

Maleh, R. (2009). Efficient Sparse Approximation Methods for Medical Imaging. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/64764

Chicago Manual of Style (16^th Edition):

Maleh, Ray. “Efficient Sparse Approximation Methods for Medical Imaging.” 2009. Doctoral Dissertation, University of Michigan. Accessed February 27, 2021. http://hdl.handle.net/2027.42/64764.

MLA Handbook (7^th Edition):

Maleh, Ray. “Efficient Sparse Approximation Methods for Medical Imaging.” 2009. Web. 27 Feb 2021.

Vancouver:

Maleh R. Efficient Sparse Approximation Methods for Medical Imaging. [Internet] [Doctoral dissertation]. University of Michigan; 2009. [cited 2021 Feb 27]. Available from: http://hdl.handle.net/2027.42/64764.

Council of Science Editors:

Maleh R. Efficient Sparse Approximation Methods for Medical Imaging. [Doctoral Dissertation]. University of Michigan; 2009. Available from: http://hdl.handle.net/2027.42/64764

27. Mortada, Hassan. Separation of parameterized and delayed sources : application to spectroscopic and multispectral data : Séparation de sources paramétriques et retardées : application aux données spectroscopiques et multispectrales.

Degree: Docteur es, Traitement du signal et des images, 2018, Université de Strasbourg

URL: http://www.theses.fr/2018STRAD051

►

Ce travail est motivé par la spectroscopie de photoélectrons et l'étude de la cinématique des galaxies où les données correspondent respectivement à une séquence temporelle… (more)

▼

Ce travail est motivé par la spectroscopie de photoélectrons et l'étude de la cinématique des galaxies où les données correspondent respectivement à une séquence temporelle de spectres et à une image multispectrale. L'objectif est d'estimer les caractéristiques (amplitude, position spectrale et paramètre de forme) des raies présentes dans les spectres, ainsi que leur évolution au sein des données. Dans les applications considérées, cette évolution est lente puisque deux spectres voisins sont souvent très similaires : c'est une connaissance a priori qui sera prise en compte dans les méthodes développées. Ce problème inverse est abordé sous l'angle de la séparation de sources retardées, où les spectres et les raies sont attribués respectivement aux mélanges et aux sources. Les méthodes de l'état de l'art sont inadéquates car elles supposent la décorrélation ou l'indépendance des sources, ce qui n'est pas le cas. Nous tirons parti de la connaissance des sources pour les modéliser par une fonction paramétrique. Nous proposons une première méthode de moindres carrés alternés : les paramètres de formes sont estimés avec l'algorithme de Levenberg-Marquardt, tandis que les amplitudes et les positions sont estimées avec un algorithme inspiré d'Orthogonal Matching Pursuit. Une deuxième méthode introduit un terme de régularisation pour prendre en compte l'évolution lente des positions; un nouvel algorithme d'approximation parcimonieuse conjointe est alors proposée. Enfin, une troisième méthode contraint l'évolution des amplitudes, positions et paramètres de forme par des fonctions B-splines afin de garantir une évolution lente conforme au physique des phénomènes observés. Les points de contrôle des B-splines sont estimés par un algorithme de moindre carrés non-linéaires. Les résultats sur des données synthétiques et réelles montrent que les méthodes proposées sont plus efficaces que les méthodes de l'état de l'art et aussi efficaces qu'une méthode bayésienne adaptée au problème mais avec un temps de calcul sensiblement réduit.

This work is motivated by photoelectron spectroscopy and the study of galaxy kinematics where data respectively correspond to a temporal sequence of spectra and a multispectral image. The objective is to estimate the characteristics (amplitude, spectral position and shape) of peaks embedded in the spectra, but also their evolution within the data. In the considered applications, this evolution is slow since two neighbor spectra are often very similar: this a priori knowledge that will be taken into account in the developed methods. This inverse problem is approached as a delayed source separation problem where spectra and peaks are respectively associated with mixtures and sources. The state-of-the-art methods are inadequate because they suppose the source decorrelation and independence, which is not the case. We take advantage of the source knowledge in order to model them by a parameterized function. We first propose an alternating least squares method: the shape parameters are estimated with the…

Advisors/Committee Members: Collet, Christophe (thesis director), Soussen, Charles (thesis director).

Subjects/Keywords: Séparation de source retardées; Mélange anéchoique; Approximation parcimonieuse; Décomposition de spectres; Images multispectrales; B-splines; Delayed source separation; Anechoic mixing; Sparse approximation; Spectra decomposition; Multispectral images; B-splines; 006.42; 519.5; 621.36

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APA (6^th Edition):

Mortada, H. (2018). Separation of parameterized and delayed sources : application to spectroscopic and multispectral data : Séparation de sources paramétriques et retardées : application aux données spectroscopiques et multispectrales. (Doctoral Dissertation). Université de Strasbourg. Retrieved from http://www.theses.fr/2018STRAD051

Chicago Manual of Style (16^th Edition):

Mortada, Hassan. “Separation of parameterized and delayed sources : application to spectroscopic and multispectral data : Séparation de sources paramétriques et retardées : application aux données spectroscopiques et multispectrales.” 2018. Doctoral Dissertation, Université de Strasbourg. Accessed February 27, 2021. http://www.theses.fr/2018STRAD051.

MLA Handbook (7^th Edition):

Mortada, Hassan. “Separation of parameterized and delayed sources : application to spectroscopic and multispectral data : Séparation de sources paramétriques et retardées : application aux données spectroscopiques et multispectrales.” 2018. Web. 27 Feb 2021.

Vancouver:

Mortada H. Separation of parameterized and delayed sources : application to spectroscopic and multispectral data : Séparation de sources paramétriques et retardées : application aux données spectroscopiques et multispectrales. [Internet] [Doctoral dissertation]. Université de Strasbourg; 2018. [cited 2021 Feb 27]. Available from: http://www.theses.fr/2018STRAD051.

Council of Science Editors:

Mortada H. Separation of parameterized and delayed sources : application to spectroscopic and multispectral data : Séparation de sources paramétriques et retardées : application aux données spectroscopiques et multispectrales. [Doctoral Dissertation]. Université de Strasbourg; 2018. Available from: http://www.theses.fr/2018STRAD051

28. Prater, Ashley. Discrete Sparse Fourier Hermite Approximations in High Dimensions.

Degree: PhD, Mathematics, 2012, Syracuse University

URL: https://surface.syr.edu/mat_etd/70

► In this dissertation, the discrete sparse Fourier Hermite approximation of a function in a specified Hilbert space of arbitrary dimension is defined, and theoretical… (more)

Subjects/Keywords: Fourier Hermite Series; Generalized Fourier Series; Hyperbolic Cross Sparse Index; Multiscale Quadrature; Pseudospectral Approximation; Spectral Approximation; Mathematics

…this Fourier Hermite basis, a sparse, discrete approximation is described, and bounds for the… …that the spectral approximation is a good approximation of f . CHAPTER 2. SPARSE FOURIER… …FN f ||2 ||f ||2 ω ≤ N κs as desired. 2.3 Hyperbolic Cross Sparse-Grid Approximation… …coefficients cn are the same as in Definition 2.9. The sparse grid approximation competes well with… …53 4.4 Discrete Sparse Approximations…

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

APA (6^th Edition):

Prater, A. (2012). Discrete Sparse Fourier Hermite Approximations in High Dimensions. (Doctoral Dissertation). Syracuse University. Retrieved from https://surface.syr.edu/mat_etd/70

Chicago Manual of Style (16^th Edition):

Prater, Ashley. “Discrete Sparse Fourier Hermite Approximations in High Dimensions.” 2012. Doctoral Dissertation, Syracuse University. Accessed February 27, 2021. https://surface.syr.edu/mat_etd/70.

MLA Handbook (7^th Edition):

Prater, Ashley. “Discrete Sparse Fourier Hermite Approximations in High Dimensions.” 2012. Web. 27 Feb 2021.

Vancouver:

Prater A. Discrete Sparse Fourier Hermite Approximations in High Dimensions. [Internet] [Doctoral dissertation]. Syracuse University; 2012. [cited 2021 Feb 27]. Available from: https://surface.syr.edu/mat_etd/70.

Council of Science Editors:

Prater A. Discrete Sparse Fourier Hermite Approximations in High Dimensions. [Doctoral Dissertation]. Syracuse University; 2012. Available from: https://surface.syr.edu/mat_etd/70

29. LI JIA. Wavelet Approximation and Image Restoration.

Degree: 2013, National University of Singapore

URL: http://scholarbank.nus.edu.sg/handle/10635/49127

Subjects/Keywords: Sparse approximation; wavelet tight frame; image restoration; split Bregman algorithm; alternating minimization algorithm; quasi-projection operator

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

APA (6^th Edition):

JIA, L. (2013). Wavelet Approximation and Image Restoration. (Thesis). National University of Singapore. Retrieved from http://scholarbank.nus.edu.sg/handle/10635/49127

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):

JIA, LI. “Wavelet Approximation and Image Restoration.” 2013. Thesis, National University of Singapore. Accessed February 27, 2021. http://scholarbank.nus.edu.sg/handle/10635/49127.

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

MLA Handbook (7^th Edition):

JIA, LI. “Wavelet Approximation and Image Restoration.” 2013. Web. 27 Feb 2021.

Vancouver:

JIA L. Wavelet Approximation and Image Restoration. [Internet] [Thesis]. National University of Singapore; 2013. [cited 2021 Feb 27]. Available from: http://scholarbank.nus.edu.sg/handle/10635/49127.

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

Council of Science Editors:

JIA L. Wavelet Approximation and Image Restoration. [Thesis]. National University of Singapore; 2013. Available from: http://scholarbank.nus.edu.sg/handle/10635/49127

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

University of Florida

30. Sakhaee, Elham. Joint Linear Inverse Problems with Sparse Solutions: Theory and Applications.

Degree: PhD, Computer Engineering - Computer and Information Science and Engineering, 2017, University of Florida

URL: https://ufdc.ufl.edu/UFE0051036

Subjects/Keywords: compressed-sensing; computed-tomography; image-reconstruction; inverse-problems; l1-regularized-problems; medical-imaging; sparse-approximation

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

APA (6^th Edition):

Sakhaee, E. (2017). Joint Linear Inverse Problems with Sparse Solutions: Theory and Applications. (Doctoral Dissertation). University of Florida. Retrieved from https://ufdc.ufl.edu/UFE0051036

Chicago Manual of Style (16^th Edition):

Sakhaee, Elham. “Joint Linear Inverse Problems with Sparse Solutions: Theory and Applications.” 2017. Doctoral Dissertation, University of Florida. Accessed February 27, 2021. https://ufdc.ufl.edu/UFE0051036.

MLA Handbook (7^th Edition):

Sakhaee, Elham. “Joint Linear Inverse Problems with Sparse Solutions: Theory and Applications.” 2017. Web. 27 Feb 2021.

Vancouver:

Sakhaee E. Joint Linear Inverse Problems with Sparse Solutions: Theory and Applications. [Internet] [Doctoral dissertation]. University of Florida; 2017. [cited 2021 Feb 27]. Available from: https://ufdc.ufl.edu/UFE0051036.

Council of Science Editors:

Sakhaee E. Joint Linear Inverse Problems with Sparse Solutions: Theory and Applications. [Doctoral Dissertation]. University of Florida; 2017. Available from: https://ufdc.ufl.edu/UFE0051036

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