Incorporating Prior Information in Compressive Online Robust Principal Component Analysis

TL;DR

This paper introduces a compressive online robust PCA method that uses prior information from previous frames to improve real-time separation of sparse and low-rank components from limited measurements, especially in video processing.

Contribution

It proposes a novel online robust PCA algorithm that incorporates multiple prior frames and provides theoretical measurement bounds for successful separation.

Findings

Outperforms existing methods in online video foreground-background separation.

Provides theoretical bounds on the number of measurements needed.

Demonstrates effectiveness through numerical experiments.

Abstract

We consider an online version of the robust Principle Component Analysis (PCA), which arises naturally in time-varying source separations such as video foreground-background separation. This paper proposes a compressive online robust PCA with prior information for recursively separating a sequences of frames into sparse and low-rank components from a small set of measurements. In contrast to conventional batch-based PCA, which processes all the frames directly, the proposed method processes measurements taken from each frame. Moreover, this method can efficiently incorporate multiple prior information, namely previous reconstructed frames, to improve the separation and thereafter, update the prior information for the next frame. We utilize multiple prior information by solving $n\text{-}\ell_{1}$ minimization for incorporating the previous sparse components and using incremental singular value decomposition ($\mathrm{SVD}$) for exploiting the previous low-rank components. We also establish theoretical bounds on the number of measurements required to guarantee successful separation under assumptions of static or slowly-changing low-rank components. Using numerical experiments, we evaluate our bounds and the performance of the proposed algorithm. In addition, we apply the proposed algorithm to online video foreground and background separation from compressive measurements. Experimental results show that the proposed method outperforms the existing methods.