A VARIATIONAL FORMULATION FOR FRAME-BASED INVERSE PROBLEMS

C. Chaux(caroline.chauxuniv-mlv.fr)
P. L. Combettes(plcmath.jussieu.fr)
J.-C. Pesquet(pesquetuniv-mlv.fr)
V. R. Wajs(rozenbaumann.jussieu.fr)

Abstract: A convex variational framework is proposed for solving inverse problems in Hilbert spaces with a priori information on the representation of the target solution in a frame. The objective function to be minimized consists of a separable term penalizing each frame coefficient individually and of a smooth term modeling the data formation model as well as other constraints. Sparsity-constrained and Bayesian formulations are examined as special cases. A splitting algorithm is presented to solve this problem and its convergence is established in infinite-dimensional spaces under mild conditions on the penalization functions, which need not be differentiable. Numerical simulations demonstrate applications to frame-based image restoration.

Keywords: Convex programming, inverse problem, frame, Hilbert space

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

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

Citation: Technical report, Universite Paris 6, 75005 paris, France.

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Entry Submitted: 01/23/2007
Entry Accepted: 01/23/2007
Entry Last Modified: 01/23/2007

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