Weighted Low Rank Approximation for Background Estimation Problems

Classical principal component analysis (PCA) is not robust to the presence of sparse outliers in the data. The use of the $\ell_1$ norm in the Robust PCA (RPCA) method successfully eliminates the weakness of PCA in separating the sparse outliers. In this paper, by sticking a simple weight to the Frobenius norm, we propose a weighted low rank (WLR) method to avoid the often computationally expensive algorithms relying on the $\ell_1$ norm. As a proof of concept, a background estimation model has been presented and compared with two $\ell_1$ norm minimization algorithms. We illustrate that as long as a simple weight matrix is inferred from the data, one can use the weighted Frobenius norm and achieve the same or better performance

Moving Target Detection Based on an Adaptive Low-Rank Sparse Decomposition

For the exact detection of moving targets in video processing, an adaptive low-rank sparse decomposition algorithm is proposed in this paper. In the paper's algorithm, the background model and the solved frame vector are first used to construct an augmented matrix, then robust principal component analysis (RPCA) is used to perform a low-rank sparse decomposition on the enhanced augmented matrix. The separated low-rank part and sparse noise correspond to the background and motion foreground of the video frame, respectively, the incremental singular value decomposition method and the current background vector are used to update the background model. The experimental results show that the algorithm can deal with complex scenes such as light changes and background motion better, and the algorithm's delay and memory consumption can be reduced effectively