A Taste of Inverse Problems: Basic Theory and Examples

Ön Kapak
SIAM, 1 Oca 2017 - 170 sayfa
Inverse problems need to be solved in order to properly interpret indirect measurements. Often, inverse problems are ill-posed and sensitive to data errors. Therefore one has to incorporate some sort of regularization to reconstruct significant information from the given data.?

A Taste of Inverse Problems: Basic Theory and Examples?presents the main achievements that have emerged in regularization theory over the past 50 years, focusing on linear ill-posed problems and the development of methods that can be applied to them. Some of this material has previously appeared only in journal articles.?This book rigorously discusses state-of-the-art inverse problems theory, focusing on numerically relevant aspects and omitting subordinate generalizations; presents diverse real-world applications, important test cases, and possible pitfalls; and treats these applications with the same rigor and depth as the theory.
 

İçindekiler

Numerical Differentiation
1
IllPosed Problems
4
Compact Operator Equations
11
The HausdorffTikhonov Lemma
17
Computerized XRay Tomography
23
The Cauchy Problem for the Laplace Equation
31
The Factorization Method in
39
Tikhonov Regularization
47
The Conjugate Gradient Method
103
The GerchbergPapoulis Algorithm
111
Inverse Source Problems
119
Appendices
127
A The Singular Value Decomposition
129
B Sobolev Spaces
133
The Poisson Equation
139
Sobolev Spaces cont
143

Tikhonovs Method
49
The Discrepancy Principle
55
Smoothing Splines
61
Deconvolution and Imaging
67
Evaluation of Unbounded Operators
75
Iterative Regularization
83
Landweber Iteration
92
The Discrepancy Principle
95
Iterative Solution of the Cauchy Problem
97
E The Fourier Transform
147
F The Conjugate Gradient Iteration
151
Bibliography Index Contents vii 11 17
155
39
156
61
157
83
158
91
159
155
161
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