title: On a general extending and constraining procedure for linear iterative methods
creator: Nicola, Auralian
creator: Petra, Stefania
creator: Popa, Constantin
creator: Schnörr, Christoph
subject: ddc-510
subject: 510 Mathematics
description: 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.
date: 2009
type: Preprint
type: info:eu-repo/semantics/preprint
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/9761/1/BIT_31_07_09.pdf
identifier: DOI:10.11588/heidok.00009761
identifier: urn:nbn:de:bsz:16-opus-97611
identifier:   Nicola, Auralian ; Petra, Stefania ; Popa, Constantin ; Schnörr, Christoph  (2009) On a general extending and constraining procedure for linear iterative methods.  [Preprint]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/9761/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: ger