Abstract: The H-TenＲPCA model is an effective method which directly processes raw multidimensional data without destroying 3D tensor structure． However，the model demands long computing time and high requirements for hardware． What’s more，the algorithm for H-TenＲPCA has no convergence guarantee in theory． Motivated by this，background and foreground before compression were reconstructed by using PTV of background video and continuity of foreground spacetime ( 3D-TV) ，and a compressed video background and foreground restoration and separation model based on PTV-TV tensor modeling was proposed，and two ADMM algorithms with guaranteed convergence were used to solve the related optimization problems． Extensive empirical studies on open data sets show that the PTV-TV model can recover the background and the foreground，and the computing time of this model is only about 2/3 of that of H-TenＲPCA． For complex dynamic background data，the PTV-TV model maintains the same peak signalto-noise ratio and image structure similarity as H-TenＲPCA model under significant time advantages．

Key words: tensor, background/foreground separation, alternating direction method of multipliers, variation