A constrained forward-backward algorithm for image recovery problems

In the solution of inverse problems, the objective is often to minimize the sum of two convex functions f and g subject to convex constraints. Recently, many works have been devoted to this problem in the unconstrained case, when f is possibly non-smooth and g is differentiable with a Lipschitz-cont...

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Bibliographic Details
Published in:Proceedings of the ... European Signal Processing Conference (EUSIPCO) pp. 1 - 5
Main Authors: Pustelnik, Nelly, Chaux, Caroline, Pesquet, Jean-Christophe
Format: Conference Proceeding
Language:English
Published: IEEE 01.08.2008
Subjects:
Convergence
Europe
Image restoration
Inverse problems
Noise
Signal processing algorithms
ISSN:2219-5491, 2219-5491
Online Access:Get full text
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Summary:In the solution of inverse problems, the objective is often to minimize the sum of two convex functions f and g subject to convex constraints. Recently, many works have been devoted to this problem in the unconstrained case, when f is possibly non-smooth and g is differentiable with a Lipschitz-continuous gradient. The use of a non-smooth penalizing function arises in particular in wavelet regularization techniques in connection with sparsity issues. In this paper, we propose a modification of the standard forward-backward algorithm, which allows us to minimize f + g over a convex constraint set C. The effectiveness of the proposed approach is illustrated in an image restoration problem involving signal-dependent noise.
ISSN:2219-5491
2219-5491