AIR Tools - A MATLAB package of algebraic iterative reconstruction methods

Per Christian Hansen, Maria Saxild-Hansen

    Research output: Contribution to journalJournal articleResearchpeer-review


    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
    Issue number8
    Pages (from-to)2167-2178
    Publication statusPublished - 2012

    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.


    • Semi-convergence
    • Relaxation parameters
    • ART methods
    • SIRT methods
    • Tomographic imaging
    • Stopping rules


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