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Convergence Properties Of The Method Of Regularization For Noisy Linear Operator Equations
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Book Synopsis Recovery Methodologies: Regularization and Sampling by : Willi Freeden
Download or read book Recovery Methodologies: Regularization and Sampling written by Willi Freeden and published by American Mathematical Society. This book was released on 2023-08-21 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this book is to introduce the reader to methodologies in recovery problems for objects, such as functions and signals, from partial or indirect information. The recovery of objects from a set of data demands key solvers of inverse and sampling problems. Until recently, connections between the mathematical areas of inverse problems and sampling were rather tenuous. However, advances in several areas of mathematical research have revealed deep common threads between them, which proves that there is a serious need for a unifying description of the underlying mathematical ideas and concepts. Freeden and Nashed present an integrated approach to resolution methodologies from the perspective of both these areas. Researchers in sampling theory will benefit from learning about inverse problems and regularization methods, while specialists in inverse problems will gain a better understanding of the point of view of sampling concepts. This book requires some basic knowledge of functional analysis, Fourier theory, geometric number theory, constructive approximation, and special function theory. By avoiding extreme technicalities and elaborate proof techniques, it is an accessible resource for students and researchers not only from applied mathematics, but also from all branches of engineering and science.
Book Synopsis Regularization Methods in Banach Spaces by : Thomas Schuster
Download or read book Regularization Methods in Banach Spaces written by Thomas Schuster and published by Walter de Gruyter. This book was released on 2012-07-30 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Regularization methods aimed at finding stable approximate solutions are a necessary tool to tackle inverse and ill-posed problems. Inverse problems arise in a large variety of applications ranging from medical imaging and non-destructive testing via finance to systems biology. Many of these problems belong to the class of parameter identification problems in partial differential equations (PDEs) and thus are computationally demanding and mathematically challenging. Hence there is a substantial need for stable and efficient solvers for this kind of problems as well as for a rigorous convergence analysis of these methods. This monograph consists of five parts. Part I motivates the importance of developing and analyzing regularization methods in Banach spaces by presenting four applications which intrinsically demand for a Banach space setting and giving a brief glimpse of sparsity constraints. Part II summarizes all mathematical tools that are necessary to carry out an analysis in Banach spaces. Part III represents the current state-of-the-art concerning Tikhonov regularization in Banach spaces. Part IV about iterative regularization methods is concerned with linear operator equations and the iterative solution of nonlinear operator equations by gradient type methods and the iteratively regularized Gauß-Newton method. Part V finally outlines the method of approximate inverse which is based on the efficient evaluation of the measured data with reconstruction kernels.
Book Synopsis Technical Report by : University of Wisconsin--Madison. Department of Statistics
Download or read book Technical Report written by University of Wisconsin--Madison. Department of Statistics and published by . This book was released on 1972 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis SIAM Journal on Numerical Analysis by : Society for Industrial and Applied Mathematics
Download or read book SIAM Journal on Numerical Analysis written by Society for Industrial and Applied Mathematics and published by . This book was released on 1977 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains research articles on the development and analysis of numerical methods, including their convergence, stability, and error analysis as well as related results in functional analysis and approximation theory. Computational experiments and new types of numerical applications are also included.
Book Synopsis Regularization in Banach Spaces - Convergence Rates Theory by : Torsten Hein
Download or read book Regularization in Banach Spaces - Convergence Rates Theory written by Torsten Hein and published by Logos Verlag Berlin GmbH. This book was released on 2010 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by their successful application in image restoring and sparsity reconstruction this manuscript deals with regularization theory of linear and nonlinear inverse and ill-posed problems in Banach space settings. Whereas regularization in Hilbert spaces has been widely studied in literature for a long period the developement and investigation of regularization methods in Banach spaces have become a field of modern research. The manuscript is twofolded. The first part deals with convergence rates theory for Tikhonov regularization as classical regularization method. In particular, generalizations of well-established results in Hilbert spaces are presented in the Banach space situation. Since the numerical effort of Tikhonov regularization in applications is rather high iterative approaches were considered as alternative regularization variants in the second part. In particular, two Gradient-type methods were presented and their behaviour concerning convergence and stability is investigated. For one of the methods, additionally, a convergence rates result is formulated. All the theoretical results are illustrated by some numerical examples.
Book Synopsis MRC Technical Summary Report by : United States. Army. Mathematics Research Center
Download or read book MRC Technical Summary Report written by United States. Army. Mathematics Research Center and published by . This book was released on 1976 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Introduction to the Mathematical Theory of Inverse Problems by : Andreas Kirsch
Download or read book An Introduction to the Mathematical Theory of Inverse Problems written by Andreas Kirsch and published by Springer Nature. This book was released on 2021-02-15 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level textbook introduces the reader to the area of inverse problems, vital to many fields including geophysical exploration, system identification, nondestructive testing, and ultrasonic tomography. It aims to expose the basic notions and difficulties encountered with ill-posed problems, analyzing basic properties of regularization methods for ill-posed problems via several simple analytical and numerical examples. The book also presents three special nonlinear inverse problems in detail: the inverse spectral problem, the inverse problem of electrical impedance tomography (EIT), and the inverse scattering problem. The corresponding direct problems are studied with respect to existence, uniqueness, and continuous dependence on parameters. Ultimately, the text discusses theoretical results as well as numerical procedures for the inverse problems, including many exercises and illustrations to complement coursework in mathematics and engineering. This updated text includes a new chapter on the theory of nonlinear inverse problems in response to the field’s growing popularity, as well as a new section on the interior transmission eigenvalue problem which complements the Sturm-Liouville problem and which has received great attention since the previous edition was published.
Book Synopsis Regularized Image Reconstruction in Parallel MRI with MATLAB by : Joseph Suresh Paul
Download or read book Regularized Image Reconstruction in Parallel MRI with MATLAB written by Joseph Suresh Paul and published by CRC Press. This book was released on 2019-11-05 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Regularization becomes an integral part of the reconstruction process in accelerated parallel magnetic resonance imaging (pMRI) due to the need for utilizing the most discriminative information in the form of parsimonious models to generate high quality images with reduced noise and artifacts. Apart from providing a detailed overview and implementation details of various pMRI reconstruction methods, Regularized image reconstruction in parallel MRI with MATLAB examples interprets regularized image reconstruction in pMRI as a means to effectively control the balance between two specific types of error signals to either improve the accuracy in estimation of missing samples, or speed up the estimation process. The first type corresponds to the modeling error between acquired and their estimated values. The second type arises due to the perturbation of k-space values in autocalibration methods or sparse approximation in the compressed sensing based reconstruction model. Features: Provides details for optimizing regularization parameters in each type of reconstruction. Presents comparison of regularization approaches for each type of pMRI reconstruction. Includes discussion of case studies using clinically acquired data. MATLAB codes are provided for each reconstruction type. Contains method-wise description of adapting regularization to optimize speed and accuracy. This book serves as a reference material for researchers and students involved in development of pMRI reconstruction methods. Industry practitioners concerned with how to apply regularization in pMRI reconstruction will find this book most useful.
Book Synopsis Ill-Posed Problems with A Priori Information by : V. V. Vasin
Download or read book Ill-Posed Problems with A Priori Information written by V. V. Vasin and published by Walter de Gruyter. This book was released on 2013-02-18 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.
Book Synopsis Nonlinear Ill-Posed Problems by : A.N. Tikhonov
Download or read book Nonlinear Ill-Posed Problems written by A.N. Tikhonov and published by Springer. This book was released on 2014-08-23 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Encyclopaedia of Mathematics by : Michiel Hazewinkel
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Book Synopsis Government Reports Announcements by :
Download or read book Government Reports Announcements written by and published by . This book was released on 1974 with total page 1332 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Encyclopaedia of Mathematics by : M. Hazewinkel
Download or read book Encyclopaedia of Mathematics written by M. Hazewinkel and published by Springer. This book was released on 2013-12-01 with total page 967 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Handbook of Mathematical Methods in Imaging by : Otmar Scherzer
Download or read book Handbook of Mathematical Methods in Imaging written by Otmar Scherzer and published by Springer Science & Business Media. This book was released on 2010-11-23 with total page 1626 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.
Book Synopsis Multidisciplinary Methods for Analysis, Optimization and Control of Complex Systems by : Vincenzo Capasso
Download or read book Multidisciplinary Methods for Analysis, Optimization and Control of Complex Systems written by Vincenzo Capasso and published by Springer Science & Business Media. This book was released on 2006-01-05 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of lecture notes of a summer school named after the late Jacques Louis Lions. The summer school was designed to alert both Academia and Industry to the increasing role of multidisciplinary methods and tools for the design of complex products in various areas of socio-economic interest. This volume offers the reader a rare opportunity of being exposed to the presentation of real industrial and societal problems together with the relevant innovative methods used.
Author :William N. Sharpe, Jr. Publisher :Springer Science & Business Media ISBN 13 :0387268839 Total Pages :1100 pages Book Rating :4.3/5 (872 download)
Book Synopsis Springer Handbook of Experimental Solid Mechanics by : William N. Sharpe, Jr.
Download or read book Springer Handbook of Experimental Solid Mechanics written by William N. Sharpe, Jr. and published by Springer Science & Business Media. This book was released on 2008-12-04 with total page 1100 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Springer Handbook of Experimental Solid Mechanics documents both the traditional techniques as well as the new methods for experimental studies of materials, components, and structures. The emergence of new materials and new disciplines, together with the escalating use of on- and off-line computers for rapid data processing and the combined use of experimental and numerical techniques have greatly expanded the capabilities of experimental mechanics. New exciting topics are included on biological materials, MEMS and NEMS, nanoindentation, digital photomechanics, photoacoustic characterization, and atomic force microscopy in experimental solid mechanics. Presenting complete instructions to various areas of experimental solid mechanics, guidance to detailed expositions in important references, and a description of state-of-the-art applications in important technical areas, this thoroughly revised and updated edition is an excellent reference to a widespread academic, industrial, and professional engineering audience.
Book Synopsis Ill-Posed Problems in Natural Sciences by : Andrei N. Tikhonov
Download or read book Ill-Posed Problems in Natural Sciences written by Andrei N. Tikhonov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-05-18 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Ill-Posed Problems in Natural Sciences".
