Introduction to Inverse Problems in Imaging

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 Cover Half Title Title Page Copyright Page Dedication Contents Preface to the first edition Preface to the second edition Author Bios Acronyms 1. Introduction Part I: Image Deconvolution 2. Examples of image blurring 3. The ill-posedness of image deconvolution 4. Quadratic Tikhonov regularization and filtering 5. Iterative regularization methods Part II: Linear Inverse Problems 6. Examples of linear inverse problems 7. Singular value decomposition (SVD) 8. Inversion methods revisited 9. Edge-preserving regularization 10. Sparsity-enforcing regularization Part III: Statistical Methods 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 References Index