A generalized Forward-Backward splitting for sums of maximal monotone operators: application to sparsity-‐regularized inverse problems
Event details
| Date | 21.06.2011 |
| Hour | 14:00 |
| Speaker | Prof. Jalal Fadili, GREYC CNRS |
| Location | |
| Category | Conferences - Seminars |
Splitting methods for maximal monotone operators have numerous applications in constructing decomposition algorithms for convex optimization and monotone variational inequalities. Splitting algorithms have an old extensive literature, but have been popularized in the signal/image processing community only recently for solving a wide range of inverse problems. In this work, we describe a general algorithm for finding a zero of the sum of n+1 maximal monotone operators over a real Hilbert space, where one of the operators is single- valued. Our splitting scheme encompasses the classical forward-backward splitting for n=1, as well as the Douglas-Rachford splitting (and its extension). We provide a detailed convergence analysis and establish stability to errors of the proposed iteration. The framework is then applied to the minimization of the composite objective function F(x)+sum_i G_i(x), where all functions are proper lower- semicontinuous and convex, and F is differentiable with a Lipschitz-continuous gradient. Many important inverse problems amount to minimizing such functions, e.g. mixed regularization, structured sparsity, etc.. We then describe several experiments and report comparison to other algorithms to demonstrate the potential applicability of our approach.
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