Discrete Inverse Problems: Insight and Algorithms (Fundamentals of Algorithms)

This book gives an introduction to the practical treatment of inverse problems by means of numerical methods, with a focus on basic mathematical and computational aspects. To solve inverse problems, we demonstrate that insight about them goes hand in hand with algorithms.

Discrete Inverse Problems: Insight and Algorithms includes a number of tutorial exercises that give the reader hands-on experience with the methods, difficulties, and challenges associated with the treatment of inverse problems. It also includes examples and figures that illustrate the theory and algorithms.

Audience: This book is written for graduate students, researchers, and professionals in engineering and other areas that depend on solving inverse problems with noisy data. The aim is to provide readers with enough background that they can solve simple inverse problems and read more advanced literature on the subject.

Contents: Preface; List of Symbols; Chapter 1: Introduction and Motivation; Chapter 2: Meet the Fredholm Integral Equation of the First Kind; Chapter 3: Getting to Business: Discretizations of Linear Inverse Problems; Chapter 4: Computational Aspects: Regularization Methods; Chapter 5: Getting Serious: Choosing the Regularization Parameter; Chapter 6: Toward Real-World Problems: Iterative Regularization; Chapter 7: Regularization Methods at Work: Solving Real Problems; Chapter 8: Beyond the 2-Norm: The Use of Discrete Smoothing Norms; Appendix A: Linear Algebra Stuff; Appendix B: Symmetric Toeplitz-Plus-Hankel Matrices and the DCT; Appendix C: Early Work on Tikhonov Regularization ; Bibliography; Index