Introduction to Inverse Problems in Imaging

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M. Bertero (University of Genova, Italy) P. Boccacci (University of Genova, Italy)

Introduction to Inverse Problems in Imaging

M. Bertero (University of Genova, Italy), P. Boccacci (University of Genova, Italy), Christine De Mol

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English

CRC Press
29 January 2024

Applied mathematics; Light (optics); Applied optics

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

By: M. Bertero (University of Genova Italy), P. Boccacci (University of Genova, Italy), Christine De Mol
Imprint: CRC Press
Country of Publication: United Kingdom
Edition: 2nd edition
Dimensions: Height: 254mm, Width: 178mm,
Weight: 453g
ISBN: 9780367467869
ISBN 10: 0367467860
Pages: 342
Publication Date: 29 January 2024
Audience: College/higher education , Further / Higher Education , A / AS level
Format: Paperback
Publisher's Status: Active

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

Mario Bertero is a Professor at the Università di Genova. Patrizia Boccacci is a Professor at the Università di Genova. Christine De Mol is a Professor at the Université libre de Bruxelles.