Linear and Nonlinear Inverse Problems with Practical Applications (Computational Science and Engineering Series)
By: Samuli Siltanen (author), Jennifer L. Muller (author)Paperback
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Inverse problems arise in practical applications whenever there is a need to interpret indirect measurements. This book explains how to identify ill-posed inverse problems arising in practice and gives a hands-on guide to designing computational solution methods for them, with related codes on an accompanying website. The guiding linear inversion examples are the problem of image deblurring, x-ray tomography, and backward parabolic problems, including heat transfer. A thorough treatment of electrical impedance tomography is used as the guiding nonlinear inversion example which combines the analytic-geometric research tradition and the regularization-based school of thought in a fruitful manner. This book is complete with exercises and project topics, making it ideal as a classroom textbook or self-study guide for graduate and advanced undergraduate students in mathematics, engineering or physics who wish to learn about computational inversion. It also acts as a useful guide for researchers who develop inversion techniques in high-tech industry.
Jennifer L. Mueller is a Professor of Mathematics and Biomedical Engineering at Colorado State University in Fort Collins, Colorado. She has served as Vice Chair and Program Director for the SIAM Activity Group on Imaging Science. Samuli Siltanen works as a Professor of Industrial Mathematics at the University of Helsinki, Finland, and is a senior scientist in the Centre of Excellence in Inverse Problems Research nominated by the Academy of Finland for the periods 2006-2011 and 2012-2017. He is President of the Finnish Inverse Problems Society.
Part I. Linear Inverse Problems: 1. Introduction; 2. Naive reconstructions and inverse crimes; 3. Ill-posedness in inverse problems; 4. Truncated singular value decomposition; 5. Tikhonov regularization; 6. Total variation regularization; 7. Besov space regularization using wavelets; 8. Discretization-invariance; 9. Practical X-ray tomography with limited data; 10. Projects; Part II. Nonlinear Inverse Problems: 11. Nonlinear inversion; 12. Electrical impedance tomography; 13. Simulation of noisy EIT data; 14. Complex geometrical optics solutions; 15. A regularized D-bar method for direct EIT; 16. Other direct solution methods for EIT; 17. Projects; Appendix A. Banach spaces and Hilbert spaces; Appendix B. Mappings and compact operators; Appendix C. Fourier transforms and Sobolev spaces; Appendix D. Iterative solution of linear equations.
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- ID: 9781611972337
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