Background and foreground modeling is a typical method in the application of computer vision. The current general “low-rank + sparse” model decomposes the frames from the video sequences into low-rank background and sparse foreground. But the sparse assumption in such a model may not conform with the reality, and the model cannot directly reflect the correlation between the background and foreground either. Thus, we present a novel model to solve this problem by decomposing the arranged data matrixDinto low-rank backgroundLand moving foregroundM. Here, we only need to give the priori assumption of the background to be low-rank and let the foreground be separated from the background as much as possible. Based on this division, we use a pair of dual norms, nuclear norm and spectral norm, to regularize the foreground and background, respectively. Furthermore, we use a reweighted function instead of the normal norm so as to get a better and faster approximation model. Detailed explanation based on linear algebra about our two models will be presented in this paper. By the observation of the experimental results, we can see that our model can get better background modeling, and even simplified versions of our algorithms perform better than mainstream techniques IALM and GoDec.
Rank-One and Transformed Sparse Decomposition for Dynamic Cardiac MRI