Dualization of Signal Recovery Problems

作者：Combettes Patrick L^*; Dinh Dung; Vu Bang Cong

来源：Set-Valued and Variational Analysis, 2010, 18(3-4): 373-404.

DOI：10.1007/s11228-010-0147-7

• Convex optimization
• Denoising
• Dictionary
• Dykstra-like algorithm
• Duality
• Forward-backward splitting
• Image reconstruction
• Image restoration
• Inverse problem
• Signal recovery
• Primal-dual algorithm
• Proximity operator
• Total variation

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.

• 出版日期2010-12