Main description:

Fully updated throughout, 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. 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, with readers needing just a rudimentary understanding of analysis, geometry, linear algebra, probability theory, and Fourier analysis. This second edition contains new chapters on quadratic, iterative, and sparsity-enforcing tikhonov regularizations in addition to maximum likelihood methods and bayesian regularization. The authors concentrate on presenting easily implementable and fast solution algorithms. With examples and exercised 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.

Key features:

* Provides an accessible introduction to the topic, whilst keeping mathematics to a minimum

* Interdisciplinary topic with growing relevance and wide-ranging applications

* Accompanied by numerical examples throughout

Author bios

Mario Bertero is a Professor Emeritus at the Universita di Genova.

Patrizia Boccacci is a Professor at the Universita di Genova.

Christine De Mol is a Professor at the Universite libre de Bruxelles.

Contents:

1. Introduction. 2. Examples of image blurring. 3. The ill-posedness of image deconvolution. 4. Quadratic tikhonov regularization. 5. Iterative regularization methods. 6. Examples of linear inverse problems. 7. Singular value decomposition (SVD). 8. Inversion methods revisited. 9. Edge-preserving regularization. 10. Sparsity-enforcing regularization. 11. Statistical approaches to linear inverse problems 12. Statistical methods in the case of additive Gaussian noise 13. Statistical methods in the case of Poisson data 14. Conclusions