ABSTRACT
Fully updated throughout and with several new chapters, this second edition of Introduction to Inverse Problems in Imaging guides advanced undergraduate and graduate students in physics, computer science, mathematics and engineering through the principles of linear inverse problems, in addition to methods of their approximate solution and their practical applications in imaging.
This second edition contains new chapters on edge-preserving and sparsity-enforcing regularization in addition to maximum likelihood methods and Bayesian regularization for Poisson data.
The level of mathematical treatment is kept as low as possible to make the book suitable for a wide range of students from different backgrounds, with readers needing just a rudimentary understanding of analysis, geometry, linear algebra, probability theory, and Fourier analysis.
The authors concentrate on presenting easily implementable and fast solution algorithms, and this second edition is accompanied by numerical examples throughout. It will provide readers with the appropriate background needed for a clear understanding of the essence of inverse problems (ill-posedness and its cure) and, consequently, for an intelligent assessment of the rapidly growing literature on these problems.
Key features:
- Provides an accessible introduction to the topic while keeping mathematics to a minimum
- Interdisciplinary topic with growing relevance and wide-ranging applications
- Accompanied by numerical examples throughout
TABLE OF CONTENTS
chapter 1|12 pages
Introduction
part I|120 pages
Image Deconvolution
chapter 142|34 pages
Examples of image blurring
chapter 3|22 pages
The ill-posedness of image deconvolution
chapter 4|34 pages
Quadratic Tikhonov regularization and filtering
chapter 5|28 pages
Iterative regularization methods
part II|124 pages
Linear Inverse Problems
chapter 1346|28 pages
Examples of linear inverse problems
chapter 7|20 pages
Singular value decomposition (SVD)
chapter 8|30 pages
Inversion methods revisited
chapter 9|24 pages
Edge-preserving regularization
chapter 10|20 pages
Sparsity-enforcing regularization
part III|66 pages
Statistical Methods