[PDF] Linear and Nonlinear Inverse Problems with Practical Applications (Computational Science and Engineering)

ISBN: 1611972337

Category: Tutorial


Posted on 2017-10-30, by luongquocchinh.

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Author: Jennifer L. Muller | Category: Mathematics | Language: English | Page: 365 | ISBN: 1611972337 | ISBN13: 9781611972337 |

Description: 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 how to design computational solution methods for them explains computational approaches in a hands-on fashion, with related codes available on a website and serves as a convenient entry point to practical inversion. The guiding linear inversion examples are the problem of image deblurring, x-ray tomography, and backward parabolic problems, including heat transfer, and electrical impedance tomography is used as the guiding nonlinear inversion example. The book s nonlinear material combines the analytic-geometric research tradition and the regularization-based school of thought in a fruitful manner, paving the way to new theorems and algorithms for nonlinear inverse problems. Furthermore, it is the only mathematical textbook with a thorough treatment of electrical impedance tomography, and these sections are suitable for beginning and experienced researchers in mathematics and engineering. Audience: Linear and Nonlinear Inverse Problems with Practical Applications is well-suited for students in mathematics, engineering, physics, or computer science who wish to learn computational inversion (inverse problems). Professors will find that the exercises and project work topics make this a suitable textbook for advanced undergraduate and graduate courses on inverse problems. Researchers developing large-scale inversion methods for linear or nonlinear inverse problems, as well as engineers working in research and development departments at high-tech companies and in electrical impedance tomography, will also find this a valuable guide. Contents Part I: Linear Inverse Problems Chapter 1: Introduction Chapter 2: Naive 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

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