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.


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:

The most recent version of the package is described in:

See also the published book:


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.