We consider the problem of foreground and background extraction from compressed-sensed (CS) surveillance video. We propose, for the first time in the literature, a principal component analysis (PCA) approach that computes the low-rank subspace of the background scene directly in the CS domain. Rather than computing the conventional L₂-norm-based principal components, which are simply the dominant left singular vectors of the CS measurement matrix, we compute the principal components under an L₁-norm maximization criterion. The background scene is then obtained by projecting the CS measurement vector onto the L₁ principal components followed by total-variation (TV) minimization image recovery. The proposed L₁-norm procedure directly carries out low-rank background representation without reconstructing the video sequence and, at the same time, exhibits significant robustness against outliers in CS measurements compared to L₂-norm PCA.

Date Published: 14 May 2015
PDF: 10 pages
Proc. SPIE 9484, Compressive Sensing IV, 94840B (14 May 2015); doi: 10.1117/12.2179722

Published in SPIE Proceedings Vol. 9484:
Compressive Sensing IV
Fauzia Ahmad, Editor(s)