TY - GEN

T1 - Exact recovery of low-rank plus compressed sparse matrices

AU - Mardani, Morteza

AU - Mateos, Gonzalo

AU - Giannakis, Georgios B.

PY - 2012/11/6

Y1 - 2012/11/6

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84868262850&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84868262850&partnerID=8YFLogxK

U2 - 10.1109/SSP.2012.6319742

DO - 10.1109/SSP.2012.6319742

M3 - Conference contribution

AN - SCOPUS:84868262850

SN - 9781467301831

T3 - 2012 IEEE Statistical Signal Processing Workshop, SSP 2012

SP - 49

EP - 52

BT - 2012 IEEE Statistical Signal Processing Workshop, SSP 2012

T2 - 2012 IEEE Statistical Signal Processing Workshop, SSP 2012

Y2 - 5 August 2012 through 8 August 2012

ER -