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Feasibility-Seeking and Superiorization Algorithms Applied to Inverse Treatment Planning in Radiation Therapy

Ran Davidi(rdavidi***at***stanford.edu)
Yair Censor(yair***at***math.haifa.ac.il)
Reinhard W. Schulte(rschulte***at***llu.edu)
Sarah Geneser(genesers***at***radonc.ucsf.edu)
Lei Xing(lei***at***stanford.edu)

Abstract: We apply the recently proposed superiorization methodology (SM) to the inverse planning problem in radiation therapy. The inverse planning problem is represented here as a constrained minimization problem of the total variation (TV) of the intensity vector over a large system of linear two-sided inequalities. The SM can be viewed conceptually as lying between feasibility-seeking for the constraints and full-fledged constrained minimization of the objective function subject to these constraints. It is based on the discovery that many feasibility-seeking algorithms (of the projection methods variety) are perturbation-resilient, and can be proactively steered toward a feasible solution of the constraints with a reduced, thus superiorized, but not necessarily minimal, objective function value.

Keywords: Feasibility-seeking, projection methods, superiorization, bounded perturbation resilience, inverse planning problem in radiation therapy.

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Applications -- Science and Engineering (Biomedical Applications )

Citation: Contemporary Mathematics, Proceedings of the Workshop on Infinite Products of Operators and Their Applications, Technion, Haifa, Israel, May 21-24, 2012, accepted for publication.

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Entry Submitted: 02/04/2014
Entry Accepted: 02/04/2014
Entry Last Modified: 02/04/2014

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