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.Comment: 10 pages, 1 figur
