Inverse Problems with Sparsity Constraints
Inverse Problems with Sparsity Constraints

Author: Dennis Trede

Publisher: Logos Verlag Berlin GmbH

Published: 2010

Total Pages: 137

ISBN-13: 3832524665

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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.

Theoretical Foundations and Numerical Methods for Sparse Recovery
Theoretical Foundations and Numerical Methods for Sparse Recovery

Author: Massimo Fornasier

Publisher: Walter de Gruyter

Published: 2010-07-30

Total Pages: 351

ISBN-13: 3110226154

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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

Advances in Hydrogeology
Advances in Hydrogeology

Author: Phoolendra K. Mishra

Publisher: Springer Science & Business Media

Published: 2013-04-16

Total Pages: 214

ISBN-13: 146146479X

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​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.​

Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science
Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science

Author: Isaac Pesenson

Publisher: Birkhäuser

Published: 2017-08-09

Total Pages: 512

ISBN-13: 3319555561

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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.

Biomedical Image Analysis and Mining Techniques for Improved Health Outcomes
Biomedical Image Analysis and Mining Techniques for Improved Health Outcomes

Author: Karâa, Wahiba Ben Abdessalem

Publisher: IGI Global

Published: 2015-11-03

Total Pages: 441

ISBN-13: 1466688122

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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.

Automatic Control, Robotics, and Information Processing
Automatic Control, Robotics, and Information Processing

Author: Piotr Kulczycki

Publisher: Springer Nature

Published: 2020-09-03

Total Pages: 843

ISBN-13: 3030485870

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This book presents a wide and comprehensive range of issues and problems in various fields of science and engineering, from both theoretical and applied perspectives. The desire to develop more effective and efficient tools and techniques for dealing with complex processes and systems has been a natural inspiration for the emergence of numerous fields of science and technology, in particular control and automation and, more recently, robotics. The contributions gathered here concern the development of methods and algorithms to determine best practices regarding broadly perceived decisions or controls. From an engineering standpoint, many of them focus on how to automate a specific process or complex system. From a tools-based perspective, several contributions address the development of analytic and algorithmic methods and techniques, devices and systems that make it possible to develop and subsequently implement the automation and robotization of crucial areas of human activity. All topics discussed are illustrated with sample applications.

Algorithms for Sparsity-Constrained Optimization
Algorithms for Sparsity-Constrained Optimization

Author: Sohail Bahmani

Publisher: Springer Science & Business Media

Published: 2013-10-07

Total Pages: 124

ISBN-13: 3319018817

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This thesis demonstrates techniques that provide faster and more accurate solutions to a variety of problems in machine learning and signal processing. The author proposes a "greedy" algorithm, deriving sparse solutions with guarantees of optimality. The use of this algorithm removes many of the inaccuracies that occurred with the use of previous models.

Applied and Industrial Mathematics in Italy III
Applied and Industrial Mathematics in Italy III

Author: Enrico De Bernardis

Publisher: World Scientific

Published: 2010

Total Pages: 590

ISBN-13: 9814280305

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This book provides an up-to-date overview of research articles in applied and industrial mathematics in Italy. This is done through the presentation of a number of investigations focusing on subjects as nonlinear optimization, life science, semiconductor industry, cultural heritage, scientific computing and others. This volume is important as it gives a report on modern applied and industrial mathematics, and will be of specific interest to the community of applied mathematicians. This book collects selected papers presented at the 9th Conference of SIMAI. The subjects discussed include image analysis methods, optimization problems, mathematics in the life sciences, differential models in applied mathematics, inverse problems, complex systems, innovative numerical methods and others. Sample Chapter(s). Chapter 1: Multichannel Wavelet Scheme for Color Image Processing (759 KB). Contents: Existence and Uniqueness for a Three Dimensional Model of Ferromagnetism (V Berti et al.); Wave Propagation in Continuously-Layered Electromagnetic Media (G Caviglia & A Morro); Mathematical Models for Biofilms on the Surface of Monuments (F Clarelli et al.); Conservation Laws with Unilateral Constraints in Traffic Modeling (R M Colombo et al.); On a Model for the Codiffusion of Isotopes (E Comparini et al.); Multiscale Models of Drug Delivery by Thin Implantable Devices (C D''Angelo & P Zunino); A Mathematical Model of Duchenne Muscular Dystrophy (G Dell''Acqua & F Castiglione); A Dissipative System Arising in Strain-Gradient Plasticity (L Giacomelli & G Tomassetti); Material Symmetry and Invariants for a 2D Fiber-Reinforced Network with Bending Stiffness (G Indelicato); Kinetic Treatment of Charge Carrier and Phonon Transport in Graphene (P Lichtenberger et al.); Mathematical Models and Numerical Simulation of Controlled Drug Release (S Minisini & L Formaggia); A Lattice Boltzmann Model on Unstructured Grids with Application in Hemodynamics (G Pontrelli et al.); Toward Analytical Contour Dynamics (G Riccardi & D Durante); Thermo-Mechanical Modeling of Ground Deformation in Volcanic Areas (D Scandura et al.); and other papers. Readership: Researchers in applied and computational mathematics.

Scale Space and Variational Methods in Computer Vision
Scale Space and Variational Methods in Computer Vision

Author: Fiorella Sgallari

Publisher: Springer Science & Business Media

Published: 2007-07-23

Total Pages: 934

ISBN-13: 3540728236

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This book constitutes the refereed proceedings of the First International Conference on Scale Space Methods and Variational Methods in Computer Vision, SSVM 2007, emanated from the joint edition of the 4th International Workshop on Variational, Geometric and Level Set Methods in Computer Vision, VLSM 2007 and the 6th International Conference on Scale Space and PDE Methods in Computer Vision, Scale-Space 2007, held in Ischia Italy, May/June 2007.