Proximal Thresholding Algorithm for Minimization over Orthonormal Bases

Authors:
Patrick L. Combettes;Jean-Christophe Pesquet
Affiliations:
-;-
Venue:
SIAM Journal on Optimization
Year:
2007

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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 we establish the strong convergence of a proximal thresholding algorithm to solve it. Numerical applications to signal recovery are demonstrated.