Sparsity regularized Principal Component Pursuit

Abstract

We study the problem of low-rank and sparse decomposition from possibly noisy observations. We propose a novel objective function with nuclear norm on the low-rank term and ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> -`norm' on the sparse term, as well as ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm on the additive noise term. When there is no dense inlier noise, the proposed method shares the same theoretical guarantee as the Principal Component Pursuit (PCP), i.e., it can recover the low-rank component and sparse component exactly with high probability. Simulations in the noisy case demonstrate that the proposed method outperforms existing state-of-the-art methods. Results on a surveillance video application further verify the effectiveness of the proposed method.