Low-rank And Sparse Matrix Decomposition For Surveillance Video

In the last decade, with the popularity of cameras and the develop-ment of Internet, we are faced with more and more surveillance video data, which results a series of problems. For example, in the era of big data, how to store mas-sive video data? How to quickly detect the abnormal fragments? How to find the related video based on some known information? Thanks to compressed sensing theory, and this paper mainly deals with low-rank and sparse matrix decomposi-tion model for surveillance video. Based on the theory of convex relaxation, and set the low-rank matrix to be rank-one, we establish a new rank-one and sparse matrix decomposition reformulation and raise modified iterative reweighted L1al-gorithm, which has improved the performance of the recovery. Next, we apply this algorithm to magnetic resonance imaging and get good performance, which will bring big benefit to patients. Based on the theory of nonconvex relaxation, we suggest to surrogate rank with S1/2norm, and Lo norm with L1/2norm, then we propose S1/2-L1/2model. Unfortunately, it is nonconvex, nonsmooth, non-Lispchtiz. However, each subproblem has a closed form solution, it is easy to give iterative half thresholding algorithm and convergence result. Finally, we conclude this paper with some remarks.