Computational Methods for Inverse Problems

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SIAM, 2002 - Mathematics - 183 pages
2 Reviews
Inverse problems arise in a number of important practical applications, ranging from biomedical imaging to seismic prospecting. This book provides the reader with a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems. It also addresses specialized topics like image reconstruction, parameter identification, total variation methods, nonnegativity constraints, and regularization parameter selection methods. Because inverse problems typically involve the estimation of certain quantities based on indirect measurements, the estimation process is often ill-posed. Regularization methods, which have been developed to deal with this ill-posedness, are carefully explained in the early chapters of Computational Methods for Inverse Problems. The book also integrates mathematical and statistical theory with applications and practical computational methods, including topics like maximum likelihood estimation and Bayesian estimation.
  

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Contents

Analytical Tools
13
Numerical Optimization Tools
29
Statistical Estimation Theory
41
Image Deblurring
59
Parameter Identification
85
Regularization Parameter Selection Methods
97
Contents xi
107
Total Variation Regularization
129
Nonnegativity Constraints
151
Bibliography
173
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Page 175 - Feasible Images and Practical Stopping Rules for Iterative Algorithms in Emission Tomography,
Page xi - Center for Research in Scientific Computation North Carolina State University Raleigh, NC 27695-8205, USA E-mail: htbanks@crscl.math.ncsu.edu F.

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