1 research outputs found
A Dictionary-Based Generalization of Robust PCA with Applications to Target Localization in Hyperspectral Imaging
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.Comment: 21 Pages; Index terms - Low-rank, Matrix Demixing, Dictionary Sparse,
Target Localization, and Robust PC