Online (and Offline) Robust PCA: Novel Algorithms and Performance Guarantees
Jinchun Zhan, Brian Lois, Namrata Vaswani

TL;DR
This paper introduces a novel online RPCA algorithm based on ReProCS, providing the first comprehensive correctness guarantees under mild assumptions, advancing real-time data separation in video analytics.
Contribution
It develops an improved online RPCA algorithm with complete performance guarantees, overcoming key limitations of previous batch and online methods.
Findings
Algorithm achieves accurate separation of low-rank and sparse components in real-time.
Provides the first full correctness guarantees for online RPCA.
Outperforms previous methods in accuracy and robustness under mild assumptions.
Abstract
In this work, we study the online robust principal components' analysis (RPCA) problem. In recent work, RPCA has been defined as a problem of separating a low-rank matrix (true data), , and a sparse matrix (outliers), , from their sum, . A more general version of this problem is to recover and from where is the matrix of unstructured small noise/corruptions. An important application where this problem occurs is in video analytics in trying to separate sparse foregrounds (e.g., moving objects) from slowly changing backgrounds. While there has been a large amount of recent work on solutions and guarantees for the batch RPCA problem, the online problem is largely open."Online" RPCA is the problem of doing the above on-the-fly with the extra assumptions that the initial subspace is accurately known and that the subspace from which is…
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Taxonomy
TopicsSparse and Compressive Sensing Techniques · Blind Source Separation Techniques · Photoacoustic and Ultrasonic Imaging
