University of Utah
Department of Mathematics
Math 5750-1 / 6880
Computational Inverse Problems
T Th 2:00 - 3:20 pm LCB 215
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Texts:
Computational Methods for Inverse Problems, Curtis Vogel, 2002 |
Matlab codes
can be downloaded from the authors' website:
http://www.math.montana.edu/~vogel/
http://www2.imm.dtu.dk/~pch/Regutools/
Syllabus
The course provides an introduction to methods of solution of ill-posed inverse and imaging problems, such as parameter estimation, signal processing, solution of integral equations, statistical inverse problems, ill-posed optimization problems, identification of coefficients of partial differential equations.
Applications are numerous, we will discuss formulations and solutions of inverse problems in medical and geophysical imaging, non-destructive testing and image processing, optical imaging and inverse scattering, optimal design, ultrasound and X-ray computed tomography, and other problems.
The studied topics and techniques are de-convolution methods, ill-posedness, various regularization techniques, choice of regularization parameters, adjoint method, iterative methods for non-linear problems, statistical estimation, non-convex optimization techniques, variational methods.
The course is addressed to graduate and senior undergraduate students in mathematics, science, and engineering.
Additional Reading
Statistical and Computational Inverse Problems, J. Kaipio and E. Somersalo, 2005
Inverse
Problem Theory and Model Parameter Estimation, A.Tarantola, 2005 (can
be downloaded from author's
website)
Geophysical Inverse Theory, R.L. Parker, 1994
Parameter Estimation and Inverse Problems,
R. Aster, B. Borchers, C. Thurber, 2005
Guillaume Bal, Lecture Notes,
Introduction
to Inverse Problems, 2004, pdf