Convex Variational Formulation with Smooth Coupling for Multicomponent Signal Decomposition and Recovery
DOI:
https://doi.org/10.4208/nmtma.2009.m9009sKeywords:
Convex optimization, denoising, image restoration, proximal algorithm, signal decomposition, signal recovery.Abstract
A convex variational formulation is proposed to solve multicomponent signal processing problems in Hilbert spaces. The cost function consists of a separable term, in which each component is modeled through its own potential, and of a coupling term, in which constraints on linear transformations of the components are penalized with smooth functionals. An algorithm with guaranteed weak convergence to a solution to the problem is provided. Various multicomponent signal decomposition and recovery applications are discussed.