AIR Tools - A MATLAB package of algebraic iterative reconstruction methods

Publication: Research - peer-reviewJournal article – Annual report year: 2010

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We present a MATLAB package with implementations of several algebraic iterative reconstruction methods for discretizations of inverse problems. These so-called row action methods rely on semi-convergence for achieving the necessary regularization of the problem. Two classes of methods are implemented: Algebraic Reconstruction Techniques (ART) and Simultaneous Iterative Reconstruction Techniques (SIRT). In addition we provide a few simplified test problems from medical and seismic tomography. For each iterative method, a number of strategies are available for choosing the relaxation parameter and the stopping rule. 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 test 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 find the optimal discrepancy parameter.
Original languageEnglish
JournalJournal of Computational and Applied Mathematics
Publication date2012
Journal number8

Bibliographical note

This work is part of the project CSI: Computational Science in Imaging, supported by grant no. 274-07-0065 from the Danish Research Council for Technology and Production Sciences.

CitationsWeb of Science® Times Cited: 10


  • Semi-convergence, Relaxation parameters, ART methods, SIRT methods, Tomographic imaging, Stopping rules
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ID: 6442213