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.

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

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