Linear and Nonlinear Inverse Problems with Practical Applications

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: 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