Research On Tensor RPCA Model With General Linear Equality Constrains

With the continuous emergence of tensor data,more and more researchers at home and abroad have pay attention to tensor optimization.Tensor models are widely applied in computer vision,machine learning,signal processing,pattern recognition an so on.This paper focuses on the tensor RPCA model with general linear equality constrains.The tensor H-TenRPCA model with a special video compression operator,is an ef-fective method which directly processes raw multidimensional data without destroying 3D tensor structure.However,the model demands long computing time and high re-quirements for hardware,what's more,the algorithm for H-TenRPCA has no convergence guarantee in theory.We propose a PTV-TV tensor model for background and foreground recovery and separation from compressed measurements.The new model leverages the time continuity of background and temporal continuity of foreground to construct a ten-sor model for compressed surveillance videos,and the optimization problem is solved by the convergent two-block ADMM algorithm.Extensive empirical studies on open data sets show that the PTV-TV model recovers the background and the foreground,and the computing time of this model is about 2/3 of that of H-TenRPCA.The comparison index shows that for the data with dynamic background,the PTV-TV model outperforms in computing time while keeps the same PSNR and SSIM as H-TenRPCA.For the tensor RPCA model with a linear equality constrain based on the tensor t-product operation,we first study the low rank tensor optimization model without sparse properties,characterize the expression of the exact solution of the low rank tensor model under mild conditions and prove the existence and uniqueness of the optimal solution of the low rank tensor model.Then,with the help of this theoretical analysis result,the optimal solution of the tensor TNN norm plus sparse 1 norm minimization optimization model is studied.Under a weaker incoherence condition,the existence and uniqueness of the optimal solution of the general linear equality constrained tensor RPCA model are theoretically given.In order to verify its numerical validity,the model is applied to the subspace clustering problem.The tensor self representation is constructed by tensor t-product operation.The open data is tested and the clustering effect is better than that of the low rank representation matrix model.