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arXiv · 1211.3754

Recursive Robust PCA or Recursive Sparse Recovery in Large but Structured Noise

Chenlu Qiu·Namrata Vaswani·Brian Lois·Leslie Hogben
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Abstract

This work studies the recursive robust principal components' analysis(PCA) problem. Here, "robust" refers to robustness to both independent and correlated sparse outliers. If the outlier is the signal-of-interest, this problem can be interpreted as one of recursively recovering a time sequence of sparse vectors, St, in the presence of large but structured noise, Lt. The structure that we assume on Lt is that Lt is dense and lies in a low dimensional subspace that is either fixed or changes "slowly enough". A key application where this problem occurs is in video surveillance where the goal is to separate a slowly changing background (Lt) from moving foreground objects (St) on-the-fly. To solve the above problem, we introduce a novel solution called Recursive Projected CS (ReProCS). Under mild assumptions, we show that, with high probability (w.h.p.), ReProCS can exactly recover the support set of St at all times; and the reconstruction errors of both St and Lt are upper bounded by a time-invariant and small value at all times.

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Chenlu Qiu, Namrata Vaswani, Brian Lois, Leslie Hogben. 2012-11-15. Recursive Robust PCA or Recursive Sparse Recovery in Large but Structured Noise. https://arxiv.org/abs/1211.3754

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