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—In the recent work of Candes et al, the problem of recovering low rank matrix corrupted by i.i.d. sparse outliers is studied and a very elegant solution, principal component pursuit, is proposed. It is motivated as a tool for video surveillance applications with the background image sequence forming the low rank part and the moving… (More)

— This paper studies the recursive robust principal components analysis 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… (More)

In recent work, Kalman Filtered Compressed Sensing (KF-CS) was proposed to causally reconstruct time sequences of sparse signals, from a limited number of " incoherent " measurements. In this work, we develop the KF-CS idea for causal reconstruction of medical image sequences from MR data. This is the first real application of KF-CS and is considerably more… (More)

—In this work, we focus on the problem of recursively recovering a time sequence of sparse signals, with time-varying sparsity patterns, from highly undersampled measurements corrupted by very large but correlated noise. It is assumed that the noise is correlated enough to have an approximately low rank covariance matrix that is either constant, or changes… (More)

—This paper designs and extensively evaluates an online algorithm, called practical recursive projected compressive sensing (Prac-ReProCS), for recovering a time sequence of sparse vectors St and a time sequence of dense vectors Lt from their sum, Mt := St + Lt, when the Lt's lie in a slowly changing low-dimensional subspace of the full space. A key… (More)

—This work studies the recursive robust principal components' analysis (PCA) problem. Here, " robust " refers to robustness to both independent and correlated sparse outliers, although we focus on the latter. A key application where this problem occurs is in video surveillance where the goal is to separate a slowly changing background from moving foreground… (More)

—This work proposes a causal and recursive algorithm for solving the " robust " principal components' analysis (PCA) problem. We primarily focus on robustness to correlated outliers. In recent work, we proposed a new way to look at this problem and showed how a key part of its solution strategy involves solving a noisy compressive sensing (CS) problem.… (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)

We study the problem of recursively recovering a time sequence of sparse vectors, St, from measurements Mt := St + Lt that are corrupted by structured noise Lt which is dense and can have large magnitude. The structure that we require is that Lt should lie in a low dimensional subspace that is either fixed or changes " slowly enough " ; and the eigenvalues… (More)

Online or recursive robust PCA can be posed as a problem of recovering a sparse vector, St, and a dense vector, Lt, which lies in a slowly changing low-dimensional subspace, from Mt := St + Lt on-the-fly as new data comes in. For initialization, it is assumed that an accurate knowledge of the subspace in which L0 lies is available. In recent works, Qiu et… (More)