Iterative Regularization Methods For Nonlinear Ill Posed Problems
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Iterative Regularization Methods for Nonlinear Ill-Posed Problems
Author: Barbara Kaltenbacher
language: en
Publisher: Walter de Gruyter
Release Date: 2008-09-25
Nonlinear inverse problems appear in many applications, and typically they lead to mathematical models that are ill-posed, i.e., they are unstable under data perturbations. Those problems require a regularization, i.e., a special numerical treatment. This book presents regularization schemes which are based on iteration methods, e.g., nonlinear Landweber iteration, level set methods, multilevel methods and Newton type methods.
Handbook of Mathematical Methods in Imaging
Author: Otmar Scherzer
language: en
Publisher: Springer Science & Business Media
Release Date: 2010-11-23
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.
Regularization Methods in Banach Spaces
Regularization methods aimed at finding stable approximate solutions are a necessary tool to tackle inverse and ill-posed problems. Usually the mathematical model of an inverse problem consists of an operator equation of the first kind and often the