AIR Tools - A MATLAB package of algebraic iterative reconstruction methods

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

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AIR Tools - A MATLAB package of algebraic iterative reconstruction methods. / Hansen, Per Christian; Saxild-Hansen, Maria.

In: Journal of Computational and Applied Mathematics, Vol. 236, No. 8, 2012, p. 2167-2178.

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

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Hansen, Per Christian; Saxild-Hansen, Maria / AIR Tools - A MATLAB package of algebraic iterative reconstruction methods.

In: Journal of Computational and Applied Mathematics, Vol. 236, No. 8, 2012, p. 2167-2178.

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

Bibtex

@article{ad638bc86b21450fbde07b87dab65dd0,
title = "AIR Tools - A MATLAB package of algebraic iterative reconstruction methods",
keywords = "Semi-convergence, Relaxation parameters, ART methods, SIRT methods, Tomographic imaging, Stopping rules",
publisher = "Elsevier BV North-Holland",
author = "Hansen, {Per Christian} and Maria Saxild-Hansen",
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.",
year = "2012",
doi = "10.1016/j.cam.2011.09.039",
volume = "236",
number = "8",
pages = "2167--2178",
journal = "Journal of Computational and Applied Mathematics",
issn = "0377-0427",

}

RIS

TY - JOUR

T1 - AIR Tools - A MATLAB package of algebraic iterative reconstruction methods

A1 - Hansen,Per Christian

A1 - Saxild-Hansen,Maria

AU - Hansen,Per Christian

AU - Saxild-Hansen,Maria

PB - Elsevier BV North-Holland

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - Semi-convergence

KW - Relaxation parameters

KW - ART methods

KW - SIRT methods

KW - Tomographic imaging

KW - Stopping rules

U2 - 10.1016/j.cam.2011.09.039

DO - 10.1016/j.cam.2011.09.039

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

IS - 8

VL - 236

SP - 2167

EP - 2178

ER -