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 -