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• W2048050794 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. Nous décrivons comment les techniques et outils d'échantillonnage compressé récemment découverts peuvent être utilisés dans les décompositions tensorielles, avec pour illustration une modélisation des signaux provenant de plusieurs antennes multicapteurs. Nous montrons qu'en posant des bornes appropriées sur une certaine mesure de séparation entre les sources rayonnantes (appelée cohérence dans le jargon de l'échantillonnage compressé), on pouvait toujours garantir l'existence et l'unicité d'une meilleure approximation de rang r du tenseur représentant le signal. Nous en déduisons aussi une variante calculable de la condition d'unicité de Kruskal, où cette cohérence apparaît comme une mesure du k-rang. Les problèmes de récupération parcimonieuse avec un dictionnaire infini continu, de représentation tensorielle de plus bas rang, et de séparation aveugle de sources sont ainsi abordés d'une seule et même façon. La décomposition du tenseur de mesures conduit à la localisation et à l'extraction simultanées des sources rayonnantes, de manière entièrement déterministe." @default.
• W2048050794 created "2016-06-24" @default.
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• W2048050794 date "2010-06-01" @default.
• W2048050794 modified "2023-10-18" @default.
• W2048050794 title "Multiarray signal processing: Tensor decomposition meets compressed sensing" @default.
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• W2048050794 doi "https://doi.org/10.1016/j.crme.2010.06.005" @default.
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