Multiarray Signal Processing: Tensor decomposition meets compressed sensing

Abstract : We discuss how recently discovered techniques and tools from compressed sensing can be used in tensor decompositions, with a view towards modeling signals from multiple arrays of multiple sensors. We show that with appropriate bounds on a measure of separation between radiating sources called coherence, one could always guarantee the existence and uniqueness of a best rank-r approximation of the tensor representing the signal. We also deduce a computationally feasible variant of Kruskal's uniqueness condition, where the coherence appears as a proxy for k-rank. Problems of sparsest recovery with an infinite continuous dictionary, lowest-rank tensor representation, and blind source separation are treated in a uniform fashion. The decomposition of the measurement tensor leads to simultaneous localization and extraction of radiating sources, in an entirely deterministic manner.
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Lek-Heng Lim, Pierre Comon. Multiarray Signal Processing: Tensor decomposition meets compressed sensing. Comptes rendus de l’Académie des sciences. Série IIb, Mécanique, Elsevier, 2010, 338 (6), pp.311--320. ⟨10.1016/j.crme.2010.06.005⟩. ⟨hal-00512271⟩

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