PROXIMAL THRESHOLDING ALGORITHM FOR MINIMIZATION OVER ORTHONORMAL BASES

Patrick L. Combettes (plcmath.jussieu.fr)
Jean-Christophe Pesquet (pesquetuniv-mlv.fr)

Abstract: The notion of soft thresholding plays a central role in problems from various areas of applied mathematics, in which the ideal solution is known to possess a sparse decomposition in some orthonormal basis. Using convex-analytical tools, we extend this notion to that of proximal thresholding and investigate its properties, providing in particular several characterizations of such thresholders. We then propose a versatile convex variational formulation for optimization over orthonormal bases that covers a wide range of problems, and establish the strong convergence of a proximal thresholding algorithm to solve it. Numerical applications to signal recovery are demonstrated.

Keywords: convex programming, proximal point, soft thresholding, strong convergence

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Infinite Dimensional Optimization (Other )

Category 3: Nonlinear Optimization (Unconstrained Optimization )

Citation: Submitted paper.

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Entry Submitted: 09/20/2006
Entry Accepted: 09/20/2006
Entry Last Modified: 09/20/2006

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