AIR Tools II: algebraic iterative reconstruction methods, improved implementation

We present a MATLAB software package with efficient, robust, and flexible implementations of algebraic iterative reconstruction (AIR) methods for computing regularized solutions to discretizations of inverse problems. These methods are of particular interest in computed tomography and similar proble...

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Vydané v:	Numerical algorithms Ročník 79; číslo 1; s. 107 - 137
Hlavní autori:	Hansen, Per Christian, Jørgensen, Jakob Sauer
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York Springer US 01.09.2018 Springer Nature B.V
Predmet:	Algebra Algorithms Computed tomography Computer Science Image reconstruction Inverse problems Iterative methods Matrix algebra Modular design Numeric Computing Numerical Analysis Original Paper Software packages Theory of Computation Tomography ART methods Column-action methods Stopping rules Algebraic iterative reconstruction Semi-convergence 65F10 65F22 Tomographic imaging SIRT methods
ISSN:	1017-1398, 1572-9265
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Abstract	We present a MATLAB software package with efficient, robust, and flexible implementations of algebraic iterative reconstruction (AIR) methods for computing regularized solutions to discretizations of inverse problems. These methods are of particular interest in computed tomography and similar problems where they easily adapt to the particular geometry of the problem. All our methods are equipped with stopping rules as well as heuristics for computing a good relaxation parameter, and we also provide several test problems from tomography. The package is intended for users who want to experiment with algebraic iterative methods and their convergence properties. The present software is a much expanded and improved version of the package AIR Tools from 2012, based on a new modular design. In addition to improved performance and memory use, we provide more flexible iterative methods, a column-action method, new test problems, new demo functions, and—perhaps most important—the ability to use function handles instead of (sparse) matrices, allowing larger problems to be handled.
AbstractList	We present a MATLAB software package with efficient, robust, and flexible implementations of algebraic iterative reconstruction (AIR) methods for computing regularized solutions to discretizations of inverse problems. These methods are of particular interest in computed tomography and similar problems where they easily adapt to the particular geometry of the problem. All our methods are equipped with stopping rules as well as heuristics for computing a good relaxation parameter, and we also provide several test problems from tomography. The package is intended for users who want to experiment with algebraic iterative methods and their convergence properties. The present software is a much expanded and improved version of the package AIR Tools from 2012, based on a new modular design. In addition to improved performance and memory use, we provide more flexible iterative methods, a column-action method, new test problems, new demo functions, and—perhaps most important—the ability to use function handles instead of (sparse) matrices, allowing larger problems to be handled. We present a MATLAB software package with efficient, robust, and flexible implementations of algebraic iterative reconstruction (AIR) methods for computing regularized solutions to discretizations of inverse problems. These methods are of particular interest in computed tomography and similar problems where they easily adapt to the particular geometry of the problem. All our methods are equipped with stopping rules as well as heuristics for computing a good relaxation parameter, and we also provide several test problems from tomography. The package is intended for users who want to experiment with algebraic iterative methods and their convergence properties. The present software is a much expanded and improved version of the package AIR Tools from 2012, based on a new modular design. In addition to improved performance and memory use, we provide more flexible iterative methods, a column-action method, new test problems, new demo functions, and—perhaps most important—the ability to use function handles instead of (sparse) matrices, allowing larger problems to be handled.
Author	Jørgensen, Jakob Sauer Hansen, Per Christian
Author_xml	– sequence: 1 givenname: Per Christian orcidid: 0000-0002-7333-7216 surname: Hansen fullname: Hansen, Per Christian email: pcha@dtu.dk organization: Department of Applied Mathematics and Computer Science, Technical University of Denmark – sequence: 2 givenname: Jakob Sauer orcidid: 0000-0001-9114-754X surname: Jørgensen fullname: Jørgensen, Jakob Sauer organization: School of Mathematics, University of Manchester
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SubjectTerms	Algebra Algorithms Computed tomography Computer Science Image reconstruction Inverse problems Iterative methods Matrix algebra Modular design Numeric Computing Numerical Analysis Original Paper Software packages Theory of Computation Tomography
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Title	AIR Tools II: algebraic iterative reconstruction methods, improved implementation
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