Regularization Tools
# Regularization Tools Version 4.1 (for MATLAB Version 7.3)

A MATLAB package for analysis and solution of discrete ill-posed problems,
developed by
Prof. Per Christian Hansen,
DTU Compute, Technical University of Denmark.
The software is available from:
- Mathwork's MATLAB Central at
this page;
please note and respect the
**BSD License** associated with this software.

### ** Background **

The software package Regularization Tools, Version 4.1 (for MATLAB
Version 7.3), consists of a collection of documented
MATLAB
functions for analysis and solution of discrete ill-posed problems.
By means of this package, the user can experiment with different
regularization strategies, compare them, and draw conclusions that would
otherwise require a major programming effort.
In addition to the analysis and solution routines, the package also
includes 12 test problems.
The package and the underlying theory is published in:

- P. C. Hansen,
* Regularization Tools: A Matlab package for analysis and
solution of discrete ill-posed problems*, Numerical Algorithms, 6
(1994), pp. 1-35.

The most recent version of the package is described in:

- P. C. Hansen,
* Regularization Tools Version 4.0 for Matlab 7.3*,
Numerical Algorithms, 46 (2007), pp. 189-194.

The test problems included in this package are outdated
- they are too simple and they do not reflect today's challenging 2D problems.
Instead, please use the 2D test problems provided in the MATLAB packages
IR Tools and
AIR Tools II.
### ** Manual **

The accompanying manual, which also includes a description of the
underlying algorithms, as well as a tutorial, is electronically available:

### ** Additional MATLAB software **

The function TVreg.m computes a 1D Total
Variation regularized solution.
The function preprocL.m can be used to preprocess an
arbitrary *L* matrix such that it conforms with the requirements in
Regularization Tools; requires that the
UTV Tools package
is installed.

The 212-times-100 helioseismology problem used in several of my
papers is available either as an m-file
helio.m or as a mat-file
helio.mat (note: some browsers try to change
the file extension when saving this mat-file).

The functions mblur.m and oblur.m
compute block Toeplitz matrices representing motion blur and out-of-focus
blur, respectively.

The function pptsvd.m computes piecewise
polynomial regularized solutions by means of the PP-TSVD algorithm.
Note that the computing time can be very large for large problems.