AIR Tools - A MATLAB Package of Algebraic Iterative Reconstruction Techniques: Version 1.0 for Matlab 7.8

Per Christian Hansen, Maria Saxild-Hansen

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    Abstract

    This collection of MATLAB software contains 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 “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. The corresponding manuscript is: • P. C. Hansen and M. Saxild-Hansen, AIR Tools – A MATLAB Package of Algebraic Iterative Reconstruction Techniques, submitted to Journal of Computational and Applied Mathematics.
    Original languageEnglish
    Place of PublicationKgs. Lyngby, Denmark
    PublisherTechnical University of Denmark, DTU Informatics, Building 321
    Publication statusPublished - 2010
    SeriesIMM-Technical Report-2010-15

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