Robust Principal Component Pursuit - Background Matrix Recovery

I recently spent some time working on a simple linear algebra problem - decompose a matrix $ M $ into a low-rank component $ L $ and a sparse component $ S $. The algorithm I used was very trivial to implement (and parallelize using map-reduce).

In this post, I will implement this very simple algorithm, explain the objective function and demonstrate its (amazing) effectiveness on a surveillance-camera dataset.

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