Low Rank And Sparse Decomposition And Its Applications Of Foreground-background Separation In Video

The low-rank and sparse decomposition?LRSD?method,which is also called robust principal component analysis,is a very effective way to obtain and represent data.While principal component analysis?PCA?can recover the original data well for data containing Gaussian noise or other noise with small amplitude.However,it has a poor effect on data recovery with non-Gaussian distribution.The low-rank and sparse decomposition emerges to solve this problem.It is assumed that the noise is sparse in the low-rank and sparse decomposition,the amplitude and strength of the noise have less influence on it,so the LRSD method is more robust.That is why LRSD has been widely used in many fields such as video foreground-background separation,face recognition,image denoising,and image alignment.Finding a more accurate approximate representation of low-rank and sparse decomposition model is always one of its core problems.It is very important and valuable to study the defects of low rank and sparse decomposition model,improve the accuracy and robustness of this method and apply it to the video foreground-background separation.This paper has carried out in-depth research on the above issues,and the main innovations are given as follows:?1?In order to improve the accuracy of low-rank matrix and considering the superiority of nonconvex approximate expression model.Truncated nonconvex low-rank and sparse decomposition?TNLRSD?based on truncated?norm is proposed.And then,the alternating direction multiplier method?ADMM?is used to solve the proposed model.Finally,a simulation experiment of low rank image denoising is carried out,and the effectiveness and superiority of the proposed method is verified through comparative experiments.?2?The low rank structure of a matrix can be regarded as the extension of sparsity on the singular value of this matrix.Considering that the nonconvex surrogate function of l₀ norm is extended to the singular value of a matrix to approximate the rank function.The nonconvex low-rank and sparse decomposition?Non LRSD?model based on the generalized nuclear norm is proposed.And then,the alternative direction multiplier method is used to solve the proposed nonconvex problem,and the convergence of the method is also analyzed.Finally,the proposed method is applied to denoise low rank image with noise,which verifies the effectiveness and superiority of the proposed method.?3?In the classic LRSD method,the nuclear norm and ₁l norm are usually used to approximate expression of low rank matrix and sparse matrix respectively.During the solving process,this expression method will have suboptimal problems,so it may not be possible to obtain the optimal results in practical applications.In order to improve the accuracy of approximate expression of low rank matrix and sparse matrix,a new method of nonconvex low-rank and sparse matrix decomposition is proposed,which is called GNNLSM,based on the consideration of the respective use of the generalized nuclear norm?GNN?and the Laplacian scale mixture?LSM?to approximate the low rank matrix and sparse matrix,and this model can adaptively select the regularization parameters.After that,the alternating direction multiplier method is used to solve the proposed model.Finally,the proposed method is used in low rank image denoising experiments with noise.The effectiveness and superiority of the proposed method is verified through comparative experiments.?4?In order to illustrate the application of proposed LRSD methods in the real scene,three improved LRSD methods are used for video foreground-background separation.Since there is a high similarity between the video frame and the frame of background,each frame in the video is regarded as a column vector,and the video background can be regarded as a data matrix with an approximate low rank structure.In addition,since the foreground object only accounts for a small part of the video,and the relationship between the foreground and the background is small,which satisfies the sparsity,so the video foreground can be regarded as a sparse matrix,and the problem of video foreground-background separation can be transformed into the low-rank and sparse decomposition problem of the video matrix.Low-rank and sparse decomposition of video matrix can complete background modeling and foreground extraction simultaneously.The three improved LRSD methods are used in the simulation experiment of video foreground-background separation and through qualitative and quantitative evaluation,the superiority and effectiveness of the proposed three LRSD methods are further verified.