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.

See also the published book:

- P. C. Hansen,
* Rank-Deficient and Discrete Ill-Posed Problems:
Numerical Aspects of Linear Inversion*, SIAM, Philadelphia, 1998.

### ** Manual **

The accompanying manual, which also includes a description of the
underlying algorithms, as well as a tutorial, is electronically available:
The hardcopy version of the manual is also available from IMM
as a Lecture Note.

### ** 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.