We consider the decomposition of a data matrix assumed to be a superposition of a low-rank matrix and a component which is sparse in a known dictionary, using a convex demixing method. We consider two sparsity structures for the sparse factor of the dictionary sparse component, namely entry-wise and column-wise sparsity, and provide a unified analysis, encompassing both undercomplete and the overcomplete dictionary cases, to show that the constituent matrices can be successfully recovered under some relatively mild conditions on incoherence, sparsity, and rank. We leverage these results to localize targets of interest in a hyperspectral (HS) image based on their spectral signature(s) using the a priori known characteristic spectral responses of the target. We corroborate our theoretical results and analyze target localization performance of our approach via experimental evaluations and comparisons to related techniques.
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Manuscript received December 13, 2018; revised November 22, 2019; accepted February 12, 2020. Date of publication March 2, 2020; date of current version March 24, 2020. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Gonzalo Mateos. This work was supported by the DARPA YFA, under Grant N66001-14-1-4047. Preliminary versions appeared in the proceedings of the 2016 IEEE Global Conference on Signal & Information Processing (GlobalSIP), 2017 Asilomar Conference on Signals, Systems, & Computers, and the 2018 IEEE International Conference on Acoustics, Speech & Signal Processing (ICASSP). (Corresponding author: Sirisha Rambhatla.) The authors are with the Department of Electrical and Computer Engineering, University of Minnesota—Twin Cities, Minneapolis, MN 55455 USA (e-mail: email@example.com; firstname.lastname@example.org; email@example.com; firstname.lastname@example.org).
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- dictionary learning
- hyperspectral imaging
- robust PCA
- sparse representation
- target localization