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Advancements in Optimal Design and Hybrid Iterative Methods for Inverse Problems

Presented by: 
Julianne Chung Virginia Polytechnic Institute and State University
Tuesday 31st October 2017 - 16:30 to 17:20
INI Seminar Room 1
In this talk, we consider two approaches to regularization. First, we describe a framework for solving inverse problems that incorporates probabilistic information in the form of training data. We provide theoretical results for the underlying Bayes risk minimization problem and discuss efficient approaches for solving the associated empirical Bayes risk minimization problem. Second, for very large-scale problems, we describe hybrid iterative approaches based on extensions of the Golub-Kahan bidiagonalization, where Tikhonov regularization is applied to the projected subproblem rather than the original problem. We show that hybrid methods have many benefits including avoiding semiconvergence behavior and being able to estimate the regularization parameter during the iterative process. Results from image processing will be presented.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons