Recovery Of Low Rank Matrix With Mixed Noise And Its Application

The Robust PCA(RPCA)model is a classic model for dealing with matrix recovery problems.It can separate low-rank matrices contaminated by sparse large noise from the observation matrix.The RPCA model’s application is very extensive,from image batch alignment to image denoising and so on.There are many excellent algorithms for solving RPCA models such as Iterative Threshold Algorithm(IT),Accelerated Approximately Gradient Algorithm(APG),and Augmented Lagrangian Multiplier Method(ALM).At present,there is no hybrid model which can deal with sparse and noisy low rank matrix.The content of this article expands on this.In the augmented Lagrangian function of the RPCA model,the F norm of the loss function term is not compact enough.We expect to find a better norm to improve the robustness and speed of the RPCA.Based on this,the innovation work of this paper has the following three points:Firstly,this paper proposed a new generalized robust principal component analysis model(GRPCA21)in order to recover low-rank matrix that are simultaneously polluted by sparse large noise and small dense noise,and the accurate solution of model is given on the basis of norm derivation.The computational process uses Randomly Permuted Multipliers Alternating Direction Multiplier Method(RP-ADMM)and gives a global convergence proof and time complexity analysis.Comparing to the excellent algorithms,for example,ALM and APG,our algorithm can obtain more robust and more accurate results on simulated data.Secondly,GRPCA21 is applied to image processing,face recognition and spam filtering.The results of image processing experiments show that our algorithm can successfully restore the low rank and mixed noise parts from the low rank matrix of mixed noise pollution,and it is superior to the ALM algorithm in detail and smoothness;The result of face recognition experiment shows that our algorithm can align many different images of the same face successfully,and can remove the ink mirror and all kinds of complex facial expressions on the face image;Based on the spam classification problem,the new generalized robust principal component analysis(GRPCA21)algorithm proposed in this paper is applied to spam filtering,and the attributes of mail are reduced by GRPCA21 before classification.Combined with the mainstream spam classification algorithm kNN and SVM,the experiments were carried out on databases containing legitimate mail and spam,and obtained high accuracy.Thirdly,taking into account the compactness of the l2,1 norm and its ability to adaptively choose the appropriate step size at iterations,the F norm is replaced by a norm in the augmented Lagrangian function of the classical RPCA model.Auxiliary matrix method is used to give a exact solution to the RPCA model based on the l2,1 norm and verify the consistency of the discrete solution obtained by the existing method.