Talk on Recursive Structured Signals Recovery and Applications in Bio-Imaging, ECE dept colloquium at UIUC, December 2013
Some key papers:
o Brian Lois and Namrata Vaswani, A Correctness Result for Online Robust PCA, submitted, on arXiv:1409.3959 [cs.IT].
o Chenlu Qiu, Namrata Vaswani, Brian Lois and Leslie Hogben, Recursive Robust PCA or Recursive Sparse Recovery in Large but Structured Noise, IEEE Trans. Information Theory, August 2014, arXiv:1211.3754v6 [cs.IT]
o Han Guo, Chenlu Qiu and Namrata Vaswani, An Online Algorithm for Separating Sparse and Low-dimensional Signal Sequences from their Sum, IEEE Trans. Signal Processing, August 2014, arXiv:1310.4261 [cs.IT] (older title: Practical ReProCS for Separating Sparse and Low-dimensional Signal Sequences from their Sum)
§ This work studies the recursive robust principal components analysis (PCA) problem. If the outlier is the signal-of-interest, this problem can be interpreted as one of recursively recovering a time sequence of sparse vectors, $S_t$, in the presence of large but structured noise, $L_t$. The structure that we assume on $L_t$ is that $L_t$ 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 ($L_t$) from moving foreground objects ($S_t$) on-the-fly.
§ To solve the above problem, in recent work, we introduced a novel solution called Recursive Projected CS (ReProCS). In this work we develop a simple modification of the original ReProCS idea and analyze it. This modification assumes knowledge of a subspace change model on the $L_t$'s. Under mild assumptions and a denseness assumption on the unestimated part of the subspace of $L_t$ at various times, we show that, with high probability (w.h.p.), the proposed approach can exactly recover the support set of $S_t$ at all times; and the reconstruction errors of both $S_t$ and $L_t$ are upper bounded by a time-invariant and small value. In simulation experiments, we observe that the last assumption holds as long as there is some support change of $S_t$ every few frames.
§ We also show extensive experiments for separating real videos into foreground and background layers on the fly. ReProCS significantly outperforms existing approaches for robust PCA when the foreground objects are large and move slowly and also when when the foreground-background intensities are similar (small magnitude nonzero sparse part). See webpages of Han Guo or Chenlu Qiu