Download or read book Inverse Problems with Sparsity Constraints written by Dennis Trede and published by Logos Verlag Berlin GmbH. This book was released on 2010 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Sparsity Constraints and Regularization for Nonlinear Inverse Problems written by Muoi-Pham Quy and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Sparsity Constraints and Regularization for Nonlinear Inverse Problems written by Muoi-Pham Quy and published by . This book was released on 2012 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Accelerated Projected Steepest Descent Method for Nonlinear Inverse Problems with Sparsity Constraints written by Gerd Teschke and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Regularization of Inverse Problems and Inexact Operator Evaluations written by Thomas Bonesky and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Regularization of Inverse Problems for Turning Processes written by Anna Christina Brandt and published by Logos Verlag Berlin. This book was released on 2013-01-24 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Advanced Techniques in Optimization for Machine Learning and Imaging written by Alessandro Benfenati and published by Springer Nature. This book was released on with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Advances in Hydrogeology written by Phoolendra K. Mishra and published by Springer Science & Business Media. This book was released on 2013-04-16 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Theoretical Foundations and Numerical Methods for Sparse Recovery written by Massimo Fornasier and published by Walter de Gruyter. This book was released on 2010-07-30 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Recent Applications of Harmonic Analysis to Function Spaces Differential Equations and Data Science written by Isaac Pesenson and published by Birkhäuser. This book was released on 2017-08-09 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Biomedical Image Analysis and Mining Techniques for Improved Health Outcomes written by Karâa, Wahiba Ben Abdessalem and published by IGI Global. This book was released on 2015-11-03 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Automatic Control Robotics and Information Processing written by Piotr Kulczycki and published by Springer Nature. This book was released on 2020-09-03 with total page 843 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Algorithms for Sparsity Constrained Optimization written by Sohail Bahmani and published by Springer Science & Business Media. This book was released on 2013-10-07 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Applied and Industrial Mathematics in Italy III written by Enrico De Bernardis and published by World Scientific. This book was released on 2010 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Scale Space and Variational Methods in Computer Vision written by Fiorella Sgallari and published by Springer Science & Business Media. This book was released on 2007-07-23 with total page 934 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Machine Intelligence and Signal Processing written by Sonali Agarwal and published by Springer Nature. This book was released on 2020-02-25 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book features selected high-quality research papers presented at the International Conference on Machine Intelligence and Signal Processing (MISP 2019), held at the Indian Institute of Technology, Allahabad, India, on September 7–10, 2019. The book covers the latest advances in the fields of machine learning, big data analytics, signal processing, computational learning theory, and their real-time applications. The topics covered include support vector machines (SVM) and variants like least-squares SVM (LS-SVM) and twin SVM (TWSVM), extreme learning machine (ELM), artificial neural network (ANN), and other areas in machine learning. Further, it discusses the real-time challenges involved in processing big data and adapting the algorithms dynamically to improve the computational efficiency. Lastly, it describes recent developments in processing signals, for instance, signals generated from IoT devices, smart systems, speech, and videos and addresses biomedical signal processing: electrocardiogram (ECG) and electroencephalogram (EEG).
Download or read book The Limits of Resolution written by Geoffrey de Villiers and published by CRC Press. This book was released on 2016-10-03 with total page 569 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This beautiful book can be read as a novel presenting carefully our quest to get more and more information from our observations and measurements. Its authors are particularly good at relating it." --Pierre C. Sabatier "This is a unique text - a labor of love pulling together for the first time the remarkably large array of mathematical and statistical techniques used for analysis of resolution in many systems of importance today – optical, acoustical, radar, etc.... I believe it will find widespread use and value." --Dr. Robert G.W. Brown, Chief Executive Officer, American Institute of Physics "The mix of physics and mathematics is a unique feature of this book which can be basic not only for PhD students but also for researchers in the area of computational imaging." --Mario Bertero, Professor, University of Geneva "a tour-de-force covering aspects of history, mathematical theory and practical applications. The authors provide a penetrating insight into the often confused topic of resolution and in doing offer a unifying approach to the subject that is applicable not only to traditional optical systems but also modern day, computer-based systems such as radar and RF communications." --Prof. Ian Proudler, Loughborough University "a ‘must have’ for anyone interested in imaging and the spatial resolution of images. This book provides detailed and very readable account of resolution in imaging and organizes the recent history of the subject in excellent fashion.... I strongly recommend it." --Michael A. Fiddy, Professor, University of North Carolina at Charlotte This book brings together the concept of resolution, which limits what we can determine about our physical world, with the theory of linear inverse problems, emphasizing practical applications. The book focuses on methods for solving illposed problems that do not have unique stable solutions. After introducing basic concepts, the contents address problems with "continuous" data in detail before turning to cases of discrete data sets. As one of the unifying principles of the text, the authors explain how non-uniqueness is a feature of measurement problems in science where precision and resolution is essentially always limited by some kind of noise.
