Discrete Ill-Posed Problems
# 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.