Here is a list of books and on-line
resources that cover many of the topics in CS
6959.
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.
- Computational Inverse Problems,
C. Vogel, SIAM Press, 2002. (This is an
excellent book on inverse problems from a
more mathematical point of view.).
- 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).
- 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
MATLAB
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.
SciPy
- Python Scripting for Computational Science by Hans Petter Langtangen,
Springer, 2004.
- Python Essential Reference (3rd Edition) by David M. Beazley,
Sams, 2006.
- Enthought Python Distribution (EPD), which includes the NumPy,
SciPy, matplotlib, mlab, Mayavi2, and other libraries, plus useful
tools such as the IPython interpreter shell (with features such
as code completion). Free for academic use.
http://www.enthought.com/products/epd.php
- SciPy tutorial:
http://www.scipy.org/SciPy_Tutorial
- NumPy tutorial:
http://www.scipy.org/Tentative_NumPy_Tutorial
- matplotlib tutorial (2D plots):
http://matplotlib.sourceforge.net/users/pyplot_tutorial.html
- mlab documentation (3D plots):
http://code.enthought.com/projects/mayavi/docs/development/html/mayavi/mlab.html
- Python documentation:
http://www.python.org/doc/
Introductory Numerical Analysis
Statistics