Low-rank and sparse decomposition of compressively-sensed matrices: applications to surveillance video processing

Abstract

Detection, recognition and tracking are three of the primary tasks involved in surveillance video processing. Given the huge amount of data generated by surveillance systems, it is desirable to use compressed sensing based techniques for acquisition and subsequent processing of videos. For compressively-sensed videos, the task of object detection can be formulated as a matrix decomposition problem, namely, decompose the video volume matrix into a low-rank background matrix and a sparse foreground matrix given a small set of linear measurements corresponding to the video volume matrix. In this thesis, we first look at three existing algorithms for low-rank and sparse matrix decomposition: Alternating Direction Method of Multipliers (ADMM), Frank-Wolfe-Projection (FW-P) and Sparse and low Rank decomposition via Compressive Sensing (SpaRCS). These algorithms do not make use of any additional structure in the data. In the case of surveillance videos, we observe that the foreground is connected in addition to being sparse. Based on this observation, we propose a regularized version of the SpaRCS algorithm, Regularized-SpaRCS (R-SpaRCS), which exploits the fact that the foreground component in surveillance videos exhibits connectedness. R-SpaRCS is a model-based greedy algorithm that introduces a support regularization step into the SpaRCS algorithm. Experiments performed on surveillance video datasets show that R-SpaRCS achieves a given recovery RSNR faster than the SpaRCS algorithm.