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SpaRCS: Recovering low-rank and sparse matrices from compressive measurements
Andrew E Waters · Aswin C Sankaranarayanan · Richard Baraniuk

Mon Dec 12 10:00 AM -- 02:59 PM (PST) @
We consider the problem of recovering a matrix $\mathbf{M}$ that is the sum of a low-rank matrix $\mathbf{L}$ and a sparse matrix $\mathbf{S}$ from a small set of linear measurements of the form $\mathbf{y} = \mathcal{A}(\mathbf{M}) = \mathcal{A}({\bf L}+{\bf S})$. 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.

Author Information

Andrew E Waters (Rice University)
Aswin C Sankaranarayanan (Rice University)
Richard Baraniuk (Rice University)

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