Compressed-Sensed-Domain L1-PCA Video Surveillance

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.