AIR Tools, Version 1.3
A MATLAB Package of Algebraic Iterative
Reconstruction Methods (for Matlab Version 8.0 or later)
July 6, 2015. This version adds a couple of new functions, and all
iterative reconstruction methods run faster and use less memory.
A bug was found in the functions fanbeamtomo,
seismicomo that caused some elements of the matrix
A to incorrectly be set to zero.
This was fixed in version 1.2.
AIR Tools is a MATLAB software package for tomographic reconstruction (and
other imaging problems) consisting of a number of algebraic
iterative reconstruction methods.
The original work was carried out as part of the project CSI: Computational
Science in Imaging, funded by the Danish Research Council for
Technology and Production Sciences, headed by
Prof. Per Christian Hansen,
The collaborators were
Dept. of Electronic Systems
at Aalborg University, and MOSEK ApS.
The development of AIR Tools continues as part of the project High-Definition
Tomography, funded by an ERC Advanced Research Grant.
The main part of the Matlab code was written by Maria Saxild-Hansen.
The core of the functions fambeamtomo, paralleltomo, and seismictomo
was written by Jakob Sauer Jørgensen.
The following people contributed to Version 1.2 with code and revisions:
Mikkel Brettschneider, Knud Cordua, Jacob Frøsig, Jakob Sauer
Jørgensen, Martin Plešinger, and Nicolai Riis.
The package includes some of the most common Algebraic Iterative
Reconstruction (AIR) methods, divided into two classes.
For all methods we provide several strategies for choosing the
relaxation parameter as well as several stopping rules.
The relaxation parameter can be fixed, or chosen adaptively
in each iteration; in the former case we provide a new "training"
algorithm that finds the optimal parameter for a given problem.
The stopping rules provided are the discrepancy principle,
the monotone error rule, and the NCP criterion; for the
first two methods "training" can be used to finde the
optimal discrepancy parameter.
The package also includes three simple test problems in
medical and seismic tomography.
The class of algebraic reconstruction techniques includes
Kaczmarz's classical method, the symmetric Kaczmarz method, and
The class of simultaneous iterative reconstruction
techniques includes Landweber's and Cimmino's classical
methods plus CAV, DROP, and SART.
Our main contribution is the design of a new training algorithms
for the optimal relaxation parameter, and the "packaging" of all
the methods with identical calling sequences and functionality
plus strategies for the various parameters and suitable stopping rules.
The package and the algorithms are described in the paper:
A course that uses this package (as well as
can be found at this page:
P. C. Hansen and M. Saxild-Hansen,
AIR Tools - A MATLAB Package of Algebraic Iterative
Reconstruction Methods, Journal of
Computational and Applied Mathematics, 236 (2012), pp. 2167-2178;
Additional test problems
- binarytomo. - creates a test problem with a
- odftomo.m - creates a test problem with a smooth