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E-grāmata: Introduction to Inverse Problems in Imaging

, (University of Genova, Italy), (University of Genova, Italy)
  • Formāts: 358 pages
  • Izdošanas datums: 20-Dec-2021
  • Izdevniecība: CRC Press
  • Valoda: eng
  • ISBN-13: 9781000516371
  • Formāts - EPUB+DRM
  • Cena: 57,60 €*
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  • Formāts: 358 pages
  • Izdošanas datums: 20-Dec-2021
  • Izdevniecība: CRC Press
  • Valoda: eng
  • ISBN-13: 9781000516371

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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
Preface to the first edition ix
Preface to the second edition xi
Author Bios xiii
Acronyms xv
1 Introduction
1(14)
Part I Image Deconvolution
2 Examples of image blurring
15(34)
3 The ill-posedness of image deconvolution
49(22)
4 Quadratic Tikhonov regularization and filtering
71(34)
5 Iterative regularization methods
105(30)
Part II Linear Inverse Problems
6 Examples of linear inverse problems
135(28)
7 Singular value decomposition (SVD)
163(20)
8 Inversion methods revisited
183(30)
9 Edge-preserving regularization
213(24)
10 Sparsity-enforcing regularization
237(22)
Part III Statistical Methods
11 Statistical approaches to linear inverse problems
259(12)
12 Statistical methods in the case of additive Gaussian noise
271(10)
13 Statistical methods in the case of Poisson data
281(26)
14 Conclusions
307(16)
References 323(14)
Index 337
Mario Bertero is a Professor at the Universitą di Genova. Patrizia Boccacci is a Professor at the Universitą di Genova. Christine De Mol is a Professor at the Université libre de Bruxelles.