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CS 6962 - Computational Inverse Problems

Here is a list of books and on-line resources that cover many of the topics in CS 6962.

Please report broken links or new resources to teach-cs6959@list.eng.utah.edu.

Inverse Problems

  • Discrete Inverse Problems: Insight and Algorithms, P.C. Hansen, SIAM Press, 2010. The main book for the course.
  • An Introduction to Inverse Problems with Applications, F.D.M. Neto and A. J. Neto, Springer, 2013. (A nice introduction to inverse theory from a mathematical point of view.).
  • Rank-Deficient and Discrete Ill-Posed Problems, P.C. Hansen, SIAM Press, 1998. (This is an excellent book on discrete linear inverse problems).
  • Linear and Nonlinear Inverse Problems with Practical Applications, Jennifer L. Müller and, Samuli Siltanen, SIAM Press, 2012. (This is very nice introductory book with several good applications).
  • Parameter Estimation and Inverse Problems, Second Edition, Richard C. Aster, Brian Borchers, and Clifford H. Thurber, Academic Press, 2012. (This is very nice introduction to inverse problems with a geophysics bent).
  • Inverse Problem Theory and Methods for Model Parameter Estimation Albert Tarantola, Siam Press, 2004. (This is a classic text on probabilistic inverse theory).
  • Geophysical Inverse Theory and Regularization Problems, Michael S. Zhdanov, Elsevier, 2002. (This is a tour de force on geophysical inverse problems written by a Utah Geophysics Professor).
  • Large-scale Inverse Problems and Quantification of Uncertainty, L Biegler, G. Biros, O. Ghattas et al. editors, Wiley, 2011. (This is a nice collection of papers on Bayesian techniques with a few large-scale applications.).
  • Optimization and Regularization for Computational Inverse Problems and Applications, Y. Wang, A.G. Yagola, and C. Yang, editors, Springer, 2010. (A collection of papers that treat inverse problems as optimization problems).
  • Inverse Problems in the Mathematical Sciences, C.W. Groetsch, Vieweg Mathematics for Scientists and Engineers, 1993. (This is a really nice introduction to inverse problems and has an excellent annotated bibliography).
  • Statistical and Computational Inverse Problems, J. Kaipio and E. Somersalo, Springer, 2005. (A nice introduction to statistical inverse theory).
  • Computational Uncertainty Quantification for Inverse Problems, Johnathan Bardsley, 2018. (A good introduction to uncertainty techniques in inverse problems).
  • Geophysical Data Analysis: Discrete Inverse Theory, W. Menke, Academic Press, 3rd edition, 2012 (A nice introduction to inverse theory within the context of geophysical problems).
  • Computational Inverse Problems in Electrocardiography, Peter R. Johnston, WIT Press, 2001. (A nice collection of articles in inverse cardiology).
  • Mathematically Modeling the Electrical Activity of the Heart: From Cell to Body Surface and Back Andrew J. Pullan, World Scientific Publishing Company, 2005. (A nice book on computational forward and inverse problems in cardiology).
  • Handbook of Neural Activity Measurement, R. Brette and A. Destexhe, editors, Cambridge University Press, 2012. (Chapter 6 of this book is on MEG and EEG source estimation).
  • Numerical Methods for the Solution of Ill-Posed Problems, A.N. Tikhonov, A.V. Goncharsky, V.V. Stepanov, and A.G. Yagola, Kluwer Academic Publishers, 1995 (a reprint of a 1990 Russian version). (This is a classic by one of the founders, Tikhonov, of regularization theory. It contains lots of Fortran code. Note that it is very expensive).
  • An Introduction to the Mathematical Theory of Inverse Problems, A. Kirsch, Springer, 1996. (A nice overview of the mathematical analysis of classical inverse problems).
  • Ill-Posed Problems: Theory and Applications, A. Bakushinsky and A. Goncharsky, Kluwer Academic Press, 1994 (a reprint of a 1989 Russian version). (A collection of chapters that use the concept of the ``regularizing algorithm'').
  • Inverse and Ill-Posed Problems, Heinz Engl and C.W. Groetsch, editors, Academic Press, 1987. (An edited collection of papers on several aspects of inverse problems including theory and applications. Thisis an often cited collection).
  • Conjugate Gradient Type Methods for Ill-Posed Problems, Martin Hanke, Pitman Research Notes in Mathematics Series 327, Longman Scientific and Technical, 1995. (This is a short monograph that contains recent efforts in iterative Krylov subspace type methods for inverse problems).
  • Ill-Posed Problems in the Natural Sciences, A.N. Tikhonov and A.V. Goncharsky, editors, MIR Publishers, 1987. (This is a nice collection of inverse application papers).
  • Regularization Methods for Ill-Posed Problems, V.A. Morozov, CRC Press, 1993. (This book is a mathematical treatise on regularization).
  • Inverse Problems in Partial Differential Equations, D. Colton, R. Ewing, and W. Rundell, editors, 1990. (A collection of application papers and applied mathematics papers on inverse problems in various pdes).
  • Plato's Cave and Inverse Problems, www.mlahanas.de/Greeks/PlatosCave.htm


SCI Institute Software

  • SCIRun Software System: A scientific problem solving environment for modeling, simulation and visualization developed by the Scientific Computing and Imaging Institute at the University of Utah.
  • SCIRun Forward/Inverse ECG Toolkit: This toolkit is a col- lection of modules and networks within the SCIRun system, which can be used to solve forward and inverse electrocardiography problems.


Introductory Numerical Analysis