Matrix ALPS: Accelerated Low Rank and Sparse Matrix Reconstruction

Details Matrix ALPS: Accelerated Low Rank and Sparse Matrix Reconstruction Matrix ALPS: Accelerated Low Rank and Sparse Matrix Reconstruction

2012-03-17

arxiv.org/abs/1203.3864v2

Computer Science

Information Theory

11 pages

Scientific paper

We propose Matrix ALPS for recovering a sparse plus low-rank decomposition of a matrix given its corrupted and incomplete linear measurements. Our approach is a first-order projected gradient method over non-convex sets, and it exploits a well-known memory-based acceleration technique. We theoretically characterize the convergence properties of Matrix ALPS using the stable embedding properties of the linear measurement operator. We then numerically illustrate that our algorithm outperforms the existing convex as well as non-convex state-of-the-art algorithms in computational efficiency without sacrificing stability.

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