Joint decomposition of multichannel signals with multimarginal optimal transport
Résumé
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, cor-
responding 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.
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