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This work studies two interrelated problems-online robust PCA (RPCA) and online low-rank matrix completion (MC). In recent work by Candès et al., RPCA has been defined as a problem of separating a low-rank matrix (true data) uses this definition of RPCA. An important application where both these problems occur is in video analytics in trying to separate… (More)

—We study the problem of recursively reconstructing a time sequence of sparse vectors St from measurements of the form Mt = ASt + BLt where A and B are known measurement matrices, and Lt lies in a slowly changing low dimensional subspace. We assume that the signal of interest (St) is sparse, and has support which is correlated over time. We introduce a… (More)

This work studies the problem of sequentially recovering a sparse vector x t and a vector from a low-dimensional subspace t from knowledge of their sum m t = x t + t. If the primary goal is to recover the low-dimensional subspace where the t 's lie, then the problem is one of online or recursive robust principal components analysis (PCA). To the best of our… (More)

In this work we develop and study a novel online robust principal components' analysis (RPCA) algorithm based on the recently introduced ReProCS framework. Our algorithm significantly improves upon the original ReProCS algorithm and it also returns even more accurate offline estimates. The key contribution of this work is a correct-ness result for this… (More)

—We study the problem of recursively reconstructing a time sequence of sparse vectors St from measurements of the form Mt = ASt + BLt where A and B are known measurement matrices, and Lt lies in a slowly changing low dimensional subspace. We assume that the signal of interest (St) is sparse, and has support which is correlated over time. We introduce a… (More)

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… (More)

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