Improvement Of Low Rank Matrix Recovery Algorithm

Robust PCA(RPCA)model can recovery low rank matrix from the matrix with sparsely highly corrupted matrix.RPCA model is widely used in many scenes,such as batch image alignment,face recognition,image denoising,data processing,video processing,etc.Since RPCA proposed,many algorithms are given to solve this model,such as the iterative threshold algorithm(IT),accelerated proximal gradient algorithm(APG)and the augmented lagrangian multiplier method(ALM).APG and ALM run faster than the original algorithm.Because of the existence of kernel functions in the RPCA model,these algorithms involve singular value decomposition.When the matrix dimension is sufficiently large,the computational complexity will become very big.In addition,there is no effective solution for the RPCA model with sparse and dense noise.Based on these two issues,the innovation of this paper has two following points:In order to improve the computational speed of the RPCA model and the robustness to outliers,this paper proposes an RPCA model with 2,1 norm.In other words,the loss function term of the augmented lagrangian multiplier method(ALM)is replaced by 2,1 norm.By 2,1 norm,the new algorithm can adaptively select the appropriate step size,which can speed up the iterative velocity.Meanwhile the 2,1 norm makes the model more robust to outliers.In the contour extraction experiment,the algorithm is four times as fast as the original algorithm.In order to solve the RPCA model(G-RPCA)with sparse big noise and dense small noise,this paper proposes Randomly Permuted ADMM(RP-ADMM)to solve this model.The global convergence of the algorithm is proved.Finally,the validity of the algorithm is proved by numerical simulation and instance verification.The results show that the proposed algorithm is faster and more robust than the existing algorithms,and it is better to separate the images when dealing with pictures that are simultaneously polluted by sparse large noise and dense small noise Low rank part,large noise part and small noise part.