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On a general extending and constraining procedure for linear iterative methods

Nicola, Auralian and Petra, Stefania and Popa, Constantin and Schnörr, Christoph

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Abstract

Algebraic Reconstruction Techniques (ART), on their both successive or simultaneous formulation, have been developed since early 70's as efficient ''row action methods'' for solving the image reconstruction problem in Computerized Tomography. In this respect, two important development directions were concerned with, firstly their extension to the inconsistent case of the reconstruction problem, and secondly with their combination with constraining strategies, imposed by the particularities of the reconstructed image. In the first part of our paper we introduce extending and constraining procedures for a general iterative method of ART type and we propose a set of sufficient assumptions that ensure the convergence of the corresponding algorithms. As an application of this approach, we prove that Cimmino's simultaneous reflections method satisfies this set of assumptions, and we derive extended and constrained versions for it. Numerical experiments with all these versions are presented on a head phantom widely used in the image reconstruction literature. We also considered hard thresholding constraining used in sparse approximation problems and applied it successfully to a 3D particle image reconstruction problem.

Item Type: Preprint
Series Name: IWR-Preprints
Date Deposited: 17. Aug 2009 07:37
Date: 2009
Faculties / Institutes: Service facilities > Interdisciplinary Center for Scientific Computing
Subjects: 510 Mathematics
Controlled Keywords: Algebraic Reconstruction Techniques, inconsistent least squares problems, constraining strategies, Cimmino algorithm, Cimmino Extended algorithm
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