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Author: Dennis Trede Publisher: Logos Verlag Berlin GmbH ISBN: 3832524665 Category : Computers Languages : en Pages : 137
Book Description
This thesis contributes to the field of inverse problems with sparsity constraints. Since the pioneering work by Daubechies, Defries and De Mol in 2004, methods for solving operator equations with sparsity constraints play a central role in the field of inverse problems. This can be explained by the fact that the solutions of many inverse problems have a sparse structure, in other words, they can be represented using only finitely many elements of a suitable basis or dictionary. Generally, to stably solve an ill-posed inverse problem one needs additional assumptions on the unknown solution--the so-called source condition. In this thesis, the sparseness stands for the source condition, and with that in mind, stability results for two different approximation methods are deduced, namely, results for the Tikhonov regularization with a sparsity-enforcing penalty and for the orthogonal matching pursuit. The practical relevance of the theoretical results is shown with two examples of convolution type, namely, an example from mass spectrometry and an example from digital holography of particles.
Author: Dennis Trede Publisher: Logos Verlag Berlin GmbH ISBN: 3832524665 Category : Computers Languages : en Pages : 137
Book Description
This thesis contributes to the field of inverse problems with sparsity constraints. Since the pioneering work by Daubechies, Defries and De Mol in 2004, methods for solving operator equations with sparsity constraints play a central role in the field of inverse problems. This can be explained by the fact that the solutions of many inverse problems have a sparse structure, in other words, they can be represented using only finitely many elements of a suitable basis or dictionary. Generally, to stably solve an ill-posed inverse problem one needs additional assumptions on the unknown solution--the so-called source condition. In this thesis, the sparseness stands for the source condition, and with that in mind, stability results for two different approximation methods are deduced, namely, results for the Tikhonov regularization with a sparsity-enforcing penalty and for the orthogonal matching pursuit. The practical relevance of the theoretical results is shown with two examples of convolution type, namely, an example from mass spectrometry and an example from digital holography of particles.
Author: Thomas Bonesky Publisher: ISBN: 9783832523107 Category : Languages : en Pages : 0
Book Description
This thesis contributes to the field of inverse problems with sparsity constraints. In recent years this has been a rapidly developing field within the theory of inverse and ill-posed problems. It turned out that solutions of many inverse problems have a sparse structure, which means that they can be represented using only a finite number of elements of a suitable basis or frame. To reconstruct these solutions, Tikhonov-type regularization schemes have been investigated intensively within the last years. The minimization schemes for the related Tikhonov functionals require the evaluation of the underlying operators and their adjoints. One of the main topics of this thesis is the investigation of such a minimization scheme assuming that the necessary operator evaluations are not calculated exactly, but are computed via an adaptive scheme. A second major part is the coupling of Morozov's discrepancy principle and Tikhonov regularization, where the classical quadratic penalty term has been substituted by a more general convex functional. Finally, a non-trivial inverse heat conduction problem from steel production is solved by a combination of iterated soft-shrinkage and an adaptive finite element method.
Author: Anna Christina Brandt Publisher: Logos Verlag Berlin ISBN: 9783832533236 Category : Languages : en Pages : 0
Book Description
In this thesis, we will focus on inverse problems appearing in ultra precise turning processes. Ultra precision turning is widely used to manufacture metallic surfaces with high surface quality. One crucial influencing factor of the surface quality is unbalances leading to vibrations of the machine structure and interaction with the cutting process. This interaction is the so-called process machine interaction. Therefore, a model is built which simulates the influence of unbalances of the machine structure and process parameters on the resulting surface of the workpiece. In order to include the process machine interaction into the model, a new force model for ultra precision turning is developed. The resulting interaction model is based on a nonlinear parameter-dependent system of ordinary differential equations. The corresponding forward model is thus described by the map connecting the input parameters to the solution of this equation system. The main part of the thesis is the inversion of the forward operator, i.e. for a given tool path on the workpiece the necessary input parameters are computed such that solving the forward model with this new input parameters results in the desired tool path. Since the forward problem is ill-posed, regularization methods with sparsity constraints are applied which promote sparse solutions. The advantage of such sparse solutions is that they limit the points of machine changes in the machine control. Two different applications are treated in detail and illustrated with various numerical examples.
Author: Phoolendra K. Mishra Publisher: Springer Science & Business Media ISBN: 146146479X Category : Science Languages : en Pages : 214
Book Description
This book represents different types of progress in hydrogeology, including conceptualization changes, different approaches to simulating groundwater flow and transport new hydrogeophysical methods. Each chapter extends or summarizes a recent development in hydrogeology, with forward-looking statements regarding the challenges and strengths that are faced. While the title and scope is broad, there are several sub-themes that connect the chapters. Themes include theoretical advances in conceptualization and modeling of hydrogeologic problems. Conceptual advances are further tempered by insights arising from observations from both field and laboratory work.
Author: Massimo Fornasier Publisher: Walter de Gruyter ISBN: 3110226154 Category : Mathematics Languages : en Pages : 351
Book Description
The present collection is the very first contribution of this type in the field of sparse recovery. Compressed sensing is one of the important facets of the broader concept presented in the book, which by now has made connections with other branches such as mathematical imaging, inverse problems, numerical analysis and simulation. The book consists of four lecture notes of courses given at the Summer School on "Theoretical Foundations and Numerical Methods for Sparse Recovery" held at the Johann Radon Institute for Computational and Applied Mathematics in Linz, Austria, in September 2009. This unique collection will be of value for a broad community and may serve as a textbook for graduate courses. From the contents: "Compressive Sensing and Structured Random Matrices" by Holger Rauhut "Numerical Methods for Sparse Recovery" by Massimo Fornasier "Sparse Recovery in Inverse Problems" by Ronny Ramlau and Gerd Teschke "An Introduction to Total Variation for Image Analysis" by Antonin Chambolle, Vicent Caselles, Daniel Cremers, Matteo Novaga and Thomas Pock
Author: Isaac Pesenson Publisher: Birkhäuser ISBN: 3319555561 Category : Mathematics Languages : en Pages : 512
Book Description
The second of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discovered links between various fields. Along with many deep theoretical results, these volumes contain numerous applications to problems in signal processing, medical imaging, geodesy, statistics, and data science. The chapters within cover an impressive range of ideas from both traditional and modern harmonic analysis, such as: the Fourier transform, Shannon sampling, frames, wavelets, functions on Euclidean spaces, analysis on function spaces of Riemannian and sub-Riemannian manifolds, Fourier analysis on manifolds and Lie groups, analysis on combinatorial graphs, sheaves, co-sheaves, and persistent homologies on topological spaces. Volume II is organized around the theme of recent applications of harmonic analysis to function spaces, differential equations, and data science, covering topics such as: The classical Fourier transform, the non-linear Fourier transform (FBI transform), cardinal sampling series and translation invariant linear systems. Recent results concerning harmonic analysis on non-Euclidean spaces such as graphs and partially ordered sets. Applications of harmonic analysis to data science and statistics Boundary-value problems for PDE's including the Runge–Walsh theorem for the oblique derivative problem of physical geodesy.
Author: Karâa, Wahiba Ben Abdessalem Publisher: IGI Global ISBN: 1466688122 Category : Medical Languages : en Pages : 441
Book Description
Every second, users produce large amounts of image data from medical and satellite imaging systems. Image mining techniques that are capable of extracting useful information from image data are becoming increasingly useful, especially in medicine and the health sciences. Biomedical Image Analysis and Mining Techniques for Improved Health Outcomes addresses major techniques regarding image processing as a tool for disease identification and diagnosis, as well as treatment recommendation. Highlighting current research intended to advance the medical field, this publication is essential for use by researchers, advanced-level students, academicians, medical professionals, and technology developers. An essential addition to the reference material available in the field of medicine, this timely publication covers a range of applied research on data mining, image processing, computational simulation, data visualization, and image retrieval.
Author: Dennis Trede
Author: Dennis Trede
Author: Muoi-Pham Quy
Author: Muoi-Pham Quy
Author: Gerd Teschke
Author: Thomas Bonesky
Author: Anna Christina Brandt
Author: Phoolendra K. Mishra
Author: Massimo Fornasier
Author: Isaac Pesenson
Author: Karâa, Wahiba Ben Abdessalem