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.

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 12|14 pages

Comments and concluding remarks

part 3|37 pages

MATHEMATICAL APPENDICES

chapter Appendix A|6 pages

Euclidean and Hilbert spaces of functions

chapter Appendix B|5 pages

Linear operators in function spaces

chapter Appendix C|6 pages

Euclidean vector spaces and matrices

chapter Appendix E|4 pages

Minimization of quadratic functionals

chapter Appendix F|4 pages

Contraction and non-expansive mappings

chapter Appendix G|3 pages

The EM method