Perturbation-resilient block-iterative projection methods with application to image reconstruction from projections

A block‐iterative projection algorithm for solving the consistent convex feasibility problem in a finite‐dimensional Euclidean space that is resilient to bounded and summable perturbations (in the sense that convergence to a feasible point is retained even if such perturbations are introduced in eac...

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Bibliographic Details
Published in:International transactions in operational research Vol. 16; no. 4; pp. 505 - 524
Main Authors: Davidi, R., Herman, G.T., Censor, Y.
Format: Journal Article
Language:English
Published: Oxford, UK Blackwell Publishing Ltd 01.07.2009
Subjects:
Algorithms
block-iterative algorithms
convex feasibility
Euclidean space
image reconstruction
Operations research
perturbation resilience
product space
projection methods
Studies
superiorization
ISSN:0969-6016, 1475-3995
Online Access:Get full text
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Summary:A block‐iterative projection algorithm for solving the consistent convex feasibility problem in a finite‐dimensional Euclidean space that is resilient to bounded and summable perturbations (in the sense that convergence to a feasible point is retained even if such perturbations are introduced in each iterative step of the algorithm) is proposed. This resilience can be used to steer the iterative process towards a feasible point that is superior in the sense of some functional on the points in the Euclidean space having a small value. The potential usefulness of this is illustrated in image reconstruction from projections, using both total variation and negative entropy as the functional.
Bibliography:istex:A3B76A7932080D73AC3F7961D95D4763E6BCA2A1
ArticleID:ITOR695
ark:/67375/WNG-69C03G74-T
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ISSN:0969-6016
1475-3995
DOI:10.1111/j.1475-3995.2009.00695.x