Iterative Optimization in Inverse Problems (Chapman & Hall/CRC Monographs and Research Notes in Mathematics) - Hardcover

Book 4 of 79: Chapman & Hall/CRC Monographs and Research Notes in Mathematics

Byrne, Charles

 
9781482222333: Iterative Optimization in Inverse Problems (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)
Hardcover
ISBN 10: 1482222337 ISBN 13: 9781482222333
Publisher: Chapman and Hall/CRC, 2014

Synopsis

Iterative Optimization in Inverse Problems brings together a number of important iterative algorithms for medical imaging, optimization, and statistical estimation. It incorporates recent work that has not appeared in other books and draws on the author’s considerable research in the field, including his recently developed class of SUMMA algorithms. Related to sequential unconstrained minimization methods, the SUMMA class includes a wide range of iterative algorithms well known to researchers in various areas, such as statistics and image processing.

Organizing the topics from general to more specific, the book first gives an overview of sequential optimization, the subclasses of auxiliary-function methods, and the SUMMA algorithms. The next three chapters present particular examples in more detail, including barrier- and penalty-function methods, proximal minimization, and forward-backward splitting. The author also focuses on fixed-point algorithms for operators on Euclidean space and then extends the discussion to include distance measures other than the usual Euclidean distance. In the final chapters, specific problems illustrate the use of iterative methods previously discussed. Most chapters contain exercises that introduce new ideas and make the book suitable for self-study.

Unifying a variety of seemingly disparate algorithms, the book shows how to derive new properties of algorithms by comparing known properties of other algorithms. This unifying approach also helps researchers―from statisticians working on parameter estimation to image scientists processing scanning data to mathematicians involved in theoretical and applied optimization―discover useful related algorithms in areas outside of their expertise.

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About the Author

Charles Byrne

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Publisher
Chapman and Hall/CRC
Publication date
2014
Language
English
ISBN 10 
1482222337
ISBN 13 
9781482222333
Binding
Hardcover
Edition number
1
Number of pages
300