Jennifer L Müller, Samuli Siltanen

Linear and Nonlinear Inverse Problems with Practical Applications

• Broschiertes Buch

Produktbeschreibung

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.

Produktdetails

• Verlag: Society for Industrial and Applied Mathematics (SIAM)
• Seitenzahl: 372
• Erscheinungstermin: 15. November 2012
• Englisch
• Abmessung: 256mm x 177mm x 22mm
• Gewicht: 637g
• ISBN-13: 9781611972337
• ISBN-10: 1611972337
• Artikelnr.: 37265081

Autorenporträt

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.

Inhaltsangabe

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