Linear and Nonlinear Inverse Problems with Practical Applications
Linear and Nonlinear Inverse Problems with Practical Applications
£65.00
GBPInverse 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.
- A convenient entry point to practical inversion
- Shows how to identify ill-posed inverse problems and design computational solution methods for them
- Explains computational approaches in a hands-on fashion, with related codes available on a website
Product details
November 2012Paperback
9781611972337
372 pages
255 × 178 × 17 mm
0.62kg
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Table of Contents
- Part I. Linear Inverse Problems:
- 1. Introduction
- 2. Naïve 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.
