Discrete Ill-Posed Problems

This PhD course at IMM is given by Prof. Per Christian Hansen. MSc students are also welcome; technically, they will follow the course as a DTU "specialkursus".

The aim of the course is to give a practical introduction to the numerical treatment of inverse problems (also known as ill-posed problems) in the form of first-kind Fredholm integral equations, with emphasis on computational and numerical aspects. Therefore, the theory is illustrated by Matlab exercises, in such a way that the student gets hands-on experience with the most common techniques and paradigms. The following topics are treated.

Inherent difficulties of inverse problems (ill-posed problems).
Discretization and numerical treatment of integral equations.
Regularization, stabilization of a solution to an inverse problem.
Numerical "tools" for the analysis and solution of inverse problems by means of regularization.
Methods for choosing the regularization parameter (i.e., the amount of regularization).
Iterative methods for large-scale problems.

Course Material

Per Christian Hansen, Discrete Ill-Posed Problems - Insight and Algorithms, A tutorial with Matlab exercises. November 2005.
A preliminary version of these lecture notes is available here.
The Matlab software package Regularization Tools.