TY - RPRT
T1 - AIR Tools - A MATLAB Package of Algebraic Iterative Reconstruction Techniques
T2 - Version 1.0 for Matlab 7.8
AU - Hansen, Per Christian
AU - Saxild-Hansen, Maria
PY - 2010
Y1 - 2010
N2 - 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.
AB - 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.
M3 - Report
T3 - IMM-Technical Report-2010-15
BT - AIR Tools - A MATLAB Package of Algebraic Iterative Reconstruction Techniques
PB - Technical University of Denmark, DTU Informatics, Building 321
CY - Kgs. Lyngby, Denmark
ER -