Compressed-Sensed-Domain L1-PCA Video Surveillance

We consider the problem of foreground and background extraction from compressed-sensed (CS) surveillance videos that are captured by a static CS camera. We propose, for the first time in the literature, a principal component analysis (PCA) approach that computes directly in the CS domain the low-rank subspace of the background scene. Rather than computing the conventional L-2-norm-based principal components, which are simply the dominant left singular vectors of the CS-domain data matrix, we compute the principal components under an L-1-norm maximization criterion. The background scene is then obtained by projecting the CS measurement vector onto the L-1 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 L-2-norm PCA. An adaptive CS-L-1-PCA method is also developed for low-latency video surveillance. Extensive experimental studies described in this paper illustrate and support the theoretical developments.