Online Tensor Robust Principal Component Analysis

Abstract

Online robust principal component analysis (RPCA) algorithms recursively decompose incoming data into low-rank and sparse components. However, they operate on data vectors and cannot directly be applied to higher-order data arrays (e.g. video frames). In this paper, we propose a new online robust PCA algorithm that preserves the multi-dimensional structure of data. Our algorithm is based on the recently proposed tensor singular value decomposition (T-SVD). We develop a convex optimization-based approach to recover the sparse component; and subsequently, update the low-rank component using incremental T-SVD. We propose an efficient tensor convolutional extension to the fast iterative shrinkage thresholding algorithm (FISTA) to produce a fast algorithm to solve this optimization problem. We demonstrate tensor-RPCA with the application of background foreground separation in a video stream. The foreground component is modeled as a sparse signal. The background component is modeled as a gradually changing low-rank subspace. Extensive experiments on real-world videos are presented and results demonstrate the effectiveness of our online tensor robust PCA.

Keywords

• Multilinear subspace learning
• tensor convolutional sparse coding
• low-rank tensor model
• tensor singular value decomposition (T-SVD)