Exact recovery of low-rank plus compressed sparse matrices

Morteza Mardani, Gonzalo Mateos, Georgios B. Giannakis

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

Given the superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, the goal of this paper is to establish conditions under which exact recovery of the low-rank and sparse components becomes possible. This fundamental identifiability task subsumes compressed sensing and the timely low-rank plus sparse matrix recovery encountered in matrix decomposition problems. Leveraging the ability of ℓ 1- and nuclear norms to recover sparse and low-rank matrices, a convex program is formulated to estimate the unknowns. Analysis and simulations confirm that the said convex program can recover the unknowns for sufficiently low-rank and sparse enough components, along with a compression matrix possessing an isometry property.

Original languageEnglish (US)
Title of host publication2012 IEEE Statistical Signal Processing Workshop, SSP 2012
Pages49-52
Number of pages4
DOIs
StatePublished - Nov 6 2012
Event2012 IEEE Statistical Signal Processing Workshop, SSP 2012 - Ann Arbor, MI, United States
Duration: Aug 5 2012Aug 8 2012

Publication series

Name2012 IEEE Statistical Signal Processing Workshop, SSP 2012

Other

Other2012 IEEE Statistical Signal Processing Workshop, SSP 2012
CountryUnited States
CityAnn Arbor, MI
Period8/5/128/8/12

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