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Linear and Nonlinear Inverse Problems with Practical Applications

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Part of Computational Science and Engineering

Authors:
Jennifer L. Müller, Colorado State University
Samuli Siltanen, University of Helsinki

Date Published: November 2012
availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
format: Paperback
isbn: 9781611972337

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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.
- 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
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Product details
- Date Published: November 2012
- format: Paperback
- isbn: 9781611972337
- length: 372 pages
- dimensions: 255 x 178 x 17 mm
- weight: 0.62kg
- availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
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.

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Authors
Jennifer L. Müller, Colorado State University
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, University of Helsinki
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.