Low Rank Matrix Recovery Algorithms And Their Applications Via Robust PCA

Principal component analysis is a powerful tool for solving large-scale scientific problems, it is widely used in signal processing, image processing, computer vision, machine learning and other fields. When data are corrupted by Gaussian white noise, principal component analysis can recover them by singular value decomposition. However, when the added noises are not Gaussian, it cannot work well. In this paper, we study the problem via robust principal component analysis, namely recovering a low-rank matrix with an unknown fraction of its entries being arbitrarily corrupted.The main innovation of this paper is reflected in the following points:Firstly, the traditional iterative threshold algorithm is complex to derive, this paper concise duality theory to the iterative threshold algorithm, and prove the iterative threshold algorithm is essentially equivalent to a gradient algorithm which is applied to the dual problem.Secondly, we combine the theory analysis and the numerical simulations to give the empirical parameter values, so we can improve the convergence speed and accuracy. In this way, iterative threshold algorithm can be used to handle larger-scale problems.Lastly, we apply the robust principal component analysis to video foreground extraction, and separate the low rank from the sparse portion. In the end, we study the characteristic of the sparse and the low rank matrix which are got from the video foreground extraction, and demonstrate the reliability of the robust principal component analysis.