AIR Tools

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, paralleltomo, and 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, DTU Compute. The collaborators were DTU Compute, 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.

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 Regularization Tools) can be found at this page:

Additional test problems