Technion Operations Research Seminar Date: December 20, 2010 ________________________________________________________________________________ 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 ________________________________________________________________________________ You can watch the rest of the seminar plan at our web site ________________________________________________________________________________ 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). --------------------------------------------------------- Technion Math. Net (TECHMATH) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: <levinas@techunix.technion.ac.il>