多阵列信号处理：张量分解遇上压缩感知
Multiarray Signal Processing: Tensor decomposition meets compressed sensing
AI总结：
本文利用压缩感知技术研究张量分解，通过引入相干性度量保证最佳秩-r近似的存在性与唯一性，并统一处理稀疏恢复、最低秩张量表示和盲源分离问题。
摘要：
我们讨论了如何将压缩感知中最近发现的技术和工具用于张量分解，以建模来自多个传感器阵列的信号。我们证明，在辐射源之间称为相干性的分离度量的适当界限下，总能保证表示信号的张量的最佳秩-r近似的存在性和唯一性。我们还推导了Kruskal唯一性条件的一个计算可行变体，其中相干性作为k-秩的代理。具有无限连续字典的最稀疏恢复、最低秩张量表示和盲源分离问题以统一的方式处理。测量张量的分解导致辐射源的同时定位和提取，完全确定性的方式。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
