SpaRCS: Recovering Low-rank and Sparse matrices from Compressive Measurements

Aswin C. Sankaranarayanan sent me the following:

Hi Igor

here is a link to a paper that is to appear in NIPS this year.

http://www.ece.rice.edu/~aew2/sparcs.html

the paper is on recovering sparse and low rank matrices from compressive measurements of their sum. Similar to Robust PCA, but with compressive measurements of the data matrix.

warm regards,

-as

Here is the paper: SpaRCS: Recovering Low-rank and Sparse matrices from Compressive Measurements by Andrew E. Waters, Aswin C. Sankaranarayanan, and Richard G. Baraniuk. The abstarct reads:

We consider the problem of recovering a matrix M that is the sum of a low-rank matrix L and a sparse matrix S from a small set of linear measurements of the form y = A(M) = A(L + S). This model subsumes three important classes of signal recovery problems: compressive sensing, affine rank minimization, and robust principal component analysis. We propose a natural optimization problem for signal recovery under this model and develop a new greedy algorithm called SpaRCS to solve it. SpaRCS inherits a number of desirable properties from the state-of-the-art CoSaMP and ADMiRA algorithms, including exponential convergence and efficient implementation. Simulation results with video compressive sensing, hyperspectral imaging, and robust matrix completion data sets demonstrate both the accuracy and efficacy of the algorithm.

The extended version is here. The code can be downloaded here and is going to be featured on the Matrix Factorization Jungle. Rich provides additonal insight here.

Thanks Aswin !

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