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Family Constraining of Iterative Algorithms

Yair Censor (yair***at***math.haifa.ac.il)
Ioana Pantelimon (ioanapantelimon***at***gmail.com)
Constantin Popa (cpopa1956***at***gmail.com)

Abstract: In constraining iterative processes, the algorithmic operator of the iterative process is pre-multiplied by a constraining operator at each iterative step. This enables the constrained algorithm, besides solving the original problem, also to find a solution that incorporates some prior knowledge about the solution. This approach has been useful in image restoration and other image processing situations when a single constraining operator was used. In the field of image reconstruction from projections a priori information about the original image, such as smoothness or that it belongs to a certain closed convex set, may be used to improve the reconstruction quality. We study here constraining of iterative processes by a family of operators rather than by a single operator.

Keywords: Iterative algorithms, constraining operator, family constraining

Category 1: Nonlinear Optimization (Nonlinear Systems and Least-Squares )

Category 2: Applications -- Science and Engineering

Citation: Revised: July 5, 2013. Numerical Algorithms, accepted for publication.

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Entry Submitted: 06/26/2013
Entry Accepted: 06/26/2013
Entry Last Modified: 07/06/2013

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