Discrete Inverse Problems: Insight and Algorithms by Per Christian Hansen - 2010

Cambridge University Press, 2010. First edition. Paperback. New. 17 X 25 cm. This acclaimed book introduces the practical treatment of inverse problems by means of numerical methods, with a focus on basic mathematical and computational aspects. To solve inverse problems, it demonstrates that insight about them and algorithms go hand in hand. Discrete Inverse Problems includes a number of tutorial exercises that give the reader hands-on experience with the methods, and challenges associated with the treatment of inverse problems. It includes carefully constructed illustrative computed examples and figures that highlight the important issues in the theory and algorithms. This book is written for graduate students, researchers, and professionals in engineering and other areas that depend on solving inverse problems with noisy data. It aims to provide readers with enough background that they can solve simple inverse problems and read more advanced literature on the subject. • Careful constructive illustrative computed examples enhance understanding • Tutorial exercises provide practice • The text can either act as a stand-alone guide to elementary inverse problem solving, or as a preparatory volume for those wishing to tackle more advanced literature Contents Preface; List of symbols; 1. Introduction and motivation; 2. Meet the Fredholm integral equation of the first kind; 3. Getting to business: discretizations of linear inverse problems; 4. Computational aspects: regularization methods; 5. Getting serious: choosing the regularization parameter; 6. Toward real-world problems: iterative regularization; 7. Regularization methods at work: solving real problems; 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. Printed Pages: 226.