Title
A multi-level preconditioned Krylov method for the efficient solution of algebraic tomographic reconstruction problems A multi-level preconditioned Krylov method for the efficient solution of algebraic tomographic reconstruction problems
Author
Faculty/Department
Faculty of Sciences. Physics
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Antwerp ,
Subject
Mathematics
Computer. Automation
Source (journal)
Journal of computational and applied mathematics. - Antwerp
Volume/pages
283(2015) , p. 1-16
ISSN
0377-0427
ISI
000351645000001
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
Classical iterative methods for tomographic reconstruction include the class of Algebraic Reconstruction Techniques (ART). Convergence of these stationary linear iterative methods is however notably slow. In this paper we propose the use of Krylov solvers for tomographic linear inversion problems. These advanced iterative methods feature fast convergence at the expense of a higher computational cost per iteration, causing them to be generally uncompetitive without the inclusion of a suitable preconditioner. Combining elements from standard multigrid (MG) solvers and the theory of wavelets, a novel wavelet-based multi-level (WMG) preconditioner is introduced, which is shown to significantly speed-up Krylov convergence. The performance of the WMG-preconditioned Krylov method is analyzed through a spectral analysis, and the approach is compared to existing methods like the classical Simultaneous Iterative Reconstruction Technique (SIRT) and unpreconditioned Krylov methods on a 2D tomographic benchmark problem. Numerical experiments are promising, showing the method to be competitive with the classical Algebraic Reconstruction Techniques in terms of convergence speed and overall performance (CPU time) as well as precision of the reconstruction.
E-info
https://repository.uantwerpen.be/docman/iruaauth/16d27e/5b5a977fc5d.pdf
Full text (open access)
https://repository.uantwerpen.be/docman/irua/5039c5/9831.pdf
E-info
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Handle