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Support-Predicted Modified-CS for Recursive Robust Principal Components' Pursuit

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. However, if the support size of the outliers becomes too large, for a given dimension of the current PC space, then the number of "measurements" available for CS may become too small. In this work, we show how to address this issue by utilizing the correlation of the outliers to predict their support at the current time; and using this as "partial support knowledge" for solving Modified-CS instead of CS.