SpaRCS: Recovering low rank and sparse matrices from compressive measurements

We consider the problem of recovering a matrix M that is the sum ofa low-rank matrix L and a sparse matrix S from a smallset of linear measurements of the form y = A(L+S).

This model subsumes three important classes ofsignal recovery problems: compressive sensing, affine rank minimization, androbust principal component analysis.We propose a natural optimization problem for signal recovery under this model and develop a new greedy recovery algorithm called SpaRCS.SpaRCS inherits a number of desirable properties from the state-of-the-artCoSaMP and ADMiRA algorithms, including exponential convergence and efficientimplementation. Simulation results with video compressive sensing,hyperspectral imaging, and robust matrix completion data sets demonstrate boththe accuracy and efficacy of the algorithm.



SpaRCS: Recovering Low-rank and Sparse matrices from Compressive Measurements
Andrew E. Waters, Aswin C. Sankaranarayanan, and Richard G. Baraniuk



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