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Keywords
(8)
Computational Efficiency
Convex Set
Image Reconstruction
Iterative Algorithm
Optimal Algorithm
Optimization Problem
Projection Method
Total Variation
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Perturbation resilience and superiorization of iterative algorithms
Perturbation resilience and superiorization of iterative algorithms,10.1088/02665611/26/6/065008,Inverse Problems,Y. Censor,R. Davidi,G. T. Herman
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Perturbation resilience and superiorization of iterative algorithms
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Y. Censor
,
R. Davidi
,
G. T. Herman
Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little demand on computer resources. For other problems, such as finding that point in the intersection at which the value of a given function is optimal, algorithms tend to need more computer memory and longer execution time. A methodology is presented whose aim is to produce automatically for an
iterative algorithm
of the first kind a 'superiorized version' of it that retains its
computational efficiency
but nevertheless goes a long way toward solving an optimization problem. This is possible to do if the original algorithm is 'perturbation resilient', which is shown to be the case for various projection algorithms for solving the consistent convex feasibility problem. The superiorized versions of such algorithms use perturbations that steer the process in the direction of a superior feasible point, which is not necessarily optimal, with respect to the given function. After presenting these intuitive ideas in a precise mathematical form, they are illustrated in
image reconstruction
from projections for two different projection algorithms superiorized for the function whose value is the
total variation
of the image.
Journal:
Inverse Problems  INVERSE PROBL
, vol. 26, no. 6, 2010
DOI:
10.1088/02665611/26/6/065008
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(24)
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