Del i serien Computational Science & Engineering

Linear and Nonlinear Inverse Problems with Practical Applications

Häftad, Engelska, 2012

1 499 kr

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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.

Produktinformation

Utgivningsdatum2012-11-30
Mått152 x 229 x undefined mm
Vikt635 g
FormatHäftad
SpråkEngelska
SerieComputational Science & Engineering
Antal sidor364
FörlagSociety for Industrial & Applied Mathematics,U.S.
ISBN9781611972337

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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 Chapter 1: Introduction Chapter 2: Naïve Reconstructions and Inverse Crimes Chapter 3: Ill-Posedness in Inverse Problems Chapter 4: Truncated Singular Value Decomposition Chapter 5: Tikhonov Regularization Chapter 6: Total Variation Regularization Chapter 7: Besov Space Regularization Using Wavelets Chapter 8: Discretization-Invariance Chapter 9: Practical X-ray Tomography with limited data Chapter 10: Projects Part II: Nonlinear Inverse Problems Chapter 11: Nonlinear Inversion Chapter 12: Electrical Impedance Tomography Chapter 13: Simulation of Noisy EIT Data Chapter 14: Complex Geometrical Optics Solutions Chapter 15: A Regularized D-bar Method for Direct EIT Chapter 16: Other Direct Solution Methods for EIT Chapter 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