Joint Decomposition of Multichannel Signals with Multimarginal Optimal Transport

The joint decomposition of a sequence of signals is addressed, where each signal is coded within a predefined dictionary. We propose a convex variational formulation involving a regularization term based on optimal transport. The latter is designed so as to promote proximity between neighboring channels. Two kinds of regularization criteria are designed, corresponding to distinct cross-channel information on the transport of dictionary atoms from one channel to another. The resulting optimization problems are reformulated as quadratic programs and solved using a proximal algorithm. The proposed approach is analyzed for a multichannel deconvolution problem.