ABSTRACT
This is a graduate textbook on the principles of linear inverse problems, methods of their approximate solution, and practical application in imaging. The level of mathematical treatment is kept as low as possible to make the book suitable for a wide range of readers from different backgrounds in science and engineering. Mathematical prerequisites are first courses in analysis, geometry, linear algebra, probability theory, and Fourier analysis. The authors concentrate on presenting easily implementable and fast solution algorithms. With examples and exercises throughout, the book will provide the reader with the appropriate background 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.
TABLE OF CONTENTS
chapter Chapter 1|16 pages
Introduction
part 1|172 pages
IMAGE DECONVOLUTION
chapter Chapter 2|31 pages
Some mathematical tools
chapter Chapter 3|25 pages
Examples of image blurring
chapter Chapter 4|23 pages
The ill-posedness of image deconvolution
chapter Chapter 5|39 pages
Regularization methods
chapter Chapter 6|31 pages
Iterative regularization methods
chapter Chapter 7|22 pages
Statistical methods
part 2|120 pages
LINEAR INVERSE IMAGING PROBLEMS
chapter Chapter 8|29 pages
Examples of linear inverse problems
chapter Chapter 9|27 pages
Singular value decomposition (SVD)
chapter Chapter 10|21 pages
Inversion methods revisited
chapter Chapter 11|27 pages
Fourier-based methods for specific problems
chapter Chapter 12|14 pages
Comments and concluding remarks
part 3|37 pages
MATHEMATICAL APPENDICES