Linear and nonlinear inverse problems with practical applications

by Mueller, Jennifer L. Siltanen, Samuli

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Title Statements

Full title :Linear and nonlinear inverse problems with practical applications / Jennifer L. Mueller, Samuli Siltanen

Edition Statements

Publication Date:2012

Publication Statements

Publisher(s):SIAM, Society for Industrial and Applied Mathematics
Place of Publication:Philadelphia, PA
Language:eng
Publication Date:2012

The Physical Object

Description:xiii, 351 s

Edition Identifiers

ISBN:9781611972337, 1611972337
oclc:ocn819673446
Dewey Decimal:515.357

Part I. Linear Inverse Problems: 1. Introduction; 2. Naive reconstructions an 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; 1 Other direct solution methods for EIT; 17. Projects; Appendix A. Banach space and Hilbert spaces; Appendix B. Mappings and compact operators; Appendix C. Fourier transforms and Sobolev spaces; Appendix D. Iterative solution of linea equations