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Comparing implementations of penalized weighted least squares sinogram restoration

Author: Forthmann, P. · Koehler, T. · Defrise, M. (Univ. Brussel) · La Riviere, P. (Univ. Chicago)
Type:article
Date:2011-07-27
Publisher: AIP (American Institute of Physics)
Institution: Philips Research
Source:Medical Physics
Identifier: MS-31.483
Keywords: sinogram restoration
Rights: (c) 2010 AIP (American Institute of Physics)

Abstract

We have explored and compared two implementation strategies for PWLS sinogram restoration:(1)A direct matrix-inversion strategy based on the closed-form so-lution to the PWLS optimization problem and(2) an iterative approach based on the conjugate-gradient algorithmObtaining optimal performance from each strategy required modifyingthe naive off-the-shelf implementations of the algorithms to exploitthe particular symmetry and sparseness of the sinogram-restorationproblem. For the closedform approach, we subdivided the large matrixinversion into smaller coup led problems and exploited sparse-nessto minimize matrix operations. For the conjugate gradient approach,we exploited sparseness and preconditioned the problem to speed con-vergence. Despite the acceleration strategies, the direct matrix-inversion approach was found to be uncompetitive with iterative approa-ches,with a computational burden an order of magnitude or more higher.The iterative conjugate-gradient approach, however, does appear promising, with computation times half that of our previous penalized-likelihood implementation.

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