Dualization of Signal Recovery Problems

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Combettes, Patrick L.
Dung, Dinh
Vu, Bang Cong
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Abstract
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In convex optimization, duality theory can sometimes lead to simpler solution methods than those resulting from direct primal analysis. In this paper, this principle is applied to a class of composite variational problems arising in particular in signal recovery. These problems are not easily amenable to solution by current methods but they feature Fenchel-Moreau-Rockafellar dual problems that can be solved by forward-backward splitting. The proposed algorithm produces simultaneously a sequence converging weakly to a dual solution, and a sequence converging strongly to the primal solution. Our framework is shown to capture and extend several existing duality-based signal recovery methods and to be applicable to a variety of new problems beyond their scope.
Keywords
Mathematics - Optimization and Control, Mathematics - Functional Analysis, 90C25, 49N15, 94A12, 94A08
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