Video foreground and background separation via Gaussian scale mixture and generalized nuclear norm based robust principal component analysis

Since one decade, robust principal component analysis (RPCA) has been the most representative problem formulation for video foreground and background separation via decomposing an observed matrix into sparse and low-rank matrices. However, existing RPCA methods still have several major limitations for video foreground and background separation including neglecting impact of noise, low approximation degree for sparse and low-rank function, neglecting spatial-temporal relation of pixels and regularization parameter selection. All these limitations reduce their performance for video foreground and background separation. Consequently, in order to solve the problems of neglecting impact of noise and low approximation accuracy, we first design a novel RPCA method based on Gaussian scale mixture and generalized nuclear norm (GSMGNN), which integrates the Gaussian scale mixture (GSM) and generalized nuclear norm (GNN). Specifically, the GSM can better describe each pixel of foreground in videos via decomposing the foreground to a standardized Gaussian random variable and a positive hidden multiplier. Meanwhile, the GNN can better approximate to the low-rank background. In addition, we extend the GSMGNN method to the robust Gaussian scale mixture and generalized nuclear norm (RGSMGNN) method against noise via inducing the noise item. And the efficient ADMM method is adopted to solve these two proposed methods via breaking them into easier handling smaller pieces. At last, experiments on challenging datasets demonstrate the better effectiveness than many other state-of-the-art methods.