基于三阶张量的 H-TenＲPCA 模型是解决压缩感知场景分离问题的有效方法，但 该模型计算时间长，对硬件要求高，求解算法在理论上没有收敛性保证． 为此，文中利用背 景视频的时间连续性( PTV) 和前景时空连续性( 3D-TV) 来重构压缩前的背景与前景，提 出了基于 PTV-TV 张量建模的压缩视频背景前景恢复与分离模型，并采用有收敛性保证 的两块 ADMM 算法来求解相关优化问题． 实验结果表明: PTV-TV 模型能够完整恢复出视 频的背景和前景，对同一视频的处理，PTV-TV 模型的计算时间仅为 H-TenＲPCA 模型的 2/3;对于复杂动态背景数据，PTV-TV 模型在明显的时间优势下保持与 H-TenＲPCA 模型 相当的峰值信噪比和图像结构相似度． 

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．