کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4638540 1632008 2015 16 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A multi-level preconditioned Krylov method for the efficient solution of algebraic tomographic reconstruction problems
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
A multi-level preconditioned Krylov method for the efficient solution of algebraic tomographic reconstruction problems
چکیده انگلیسی

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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 283, 1 August 2015, Pages 1–16
نویسندگان
, , , , ,