Technion
 
Operations Research Seminar
 
Date: December 20, 2010
 
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Speaker: Yair Censor from University of Haifa
 
Title: Perturbation Resilience and the Superiorization Methodology
Applied to Projection methods in Image Reconstruction
 
Time and place: at 12:30 in Bloomfield-527
 
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You can watch the rest of the seminar plan at our web site
 
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For an abstract please see below, or the website of the Operations Research seminar:
 
 <http://iew3.technion.ac.il/Labs/Seminar/seminar.php?7>
 
Abstract: Superiorization is envisioned as lying in-between the
methodologies of optimization and of feasibility seeking. Generally
speaking, it is natural to assume that optimization is a computationally
more demanding task than that of finding just any feasible point. We
propose that, without employing an optimization algorithm, it is possible
to use certain iterative methods, designed for (the less demanding)
feasibility problems, in a way that will steer the iterates toward a
point that is superior, but not necessarily optimal, in a well-defined
sense. The possibility to do so stems from the perturbation resilience
(stability) of the feasibility seeking methods. Block-iterative
projection as well as string-averaging projection algorithms for solving
the consistent convex feasibility problem in a finite-dimensional
Euclidean space are 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. The
usefulness of this is illustrated in image reconstruction from
projections using total variation as the functional that leads the
superiorization. Y. Censor, R. Davidi and G.T. Herman, Perturbation
resilience and superiorization of iterative algorithms, Inverse Problems,
Vol. 26 (2010) 065008 (12pp).
 
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