Convex Variational Formulation with Smooth Coupling for Multicomponent Signal Decomposition and Recovery

摘要

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.