A multi-level preconditioned Krylov method for the efficient solution of algebraic tomographic reconstruction problems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:283

Article

Cools, Siegfried¹  Ghysels, Pieter²  van Aarle, Wim³  Sijbers, Jan³  Vanroose, Wim¹ 

[1] Univ Antwerp, Appl Math Grp, B-2020 Antwerp, Belgium

[2] Univ Calif Berkeley, Lawrence Berkeley Natl Lab, Computat Res Div, Future Technol Grp, Berkeley, CA 94720 USA

[3] Univ Antwerp, IMinds Vis Lab, B-2610 Antwerp, Belgium

关键词: Tomography;    Algebraic reconstruction;    Krylov methods;    Preconditioning;    Multigrid;    Wavelets;   

DOI  :  10.1016/j.cam.2014.12.044

来源: Elsevier

【 摘 要 】

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. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free