不完全鲁棒主成分分析的正则化方法及其在背景建模中的应用

Regularized approach for incomplete robust principal component analysis and its applications in background modeling

针对现有的鲁棒主成分分析(RPCA)方法忽略序列数据的连续性及不完整性的情况,提出了一种低秩矩阵恢复模型——正则化不完全鲁棒主成分分析(RIRPCA)。首先基于序列数据连续性的度量函数建立了RIRPCA模型,即最小化矩阵核范数、L1范数和正则项的加权组合;然后使用增广拉格朗日乘子法来求解所提出的凸优化模型,此算法具有良好的可扩展性和较低的计算复杂度;最后,将RIRPCA应用到视频背景建模中。实验结果表明,RIRPCA比矩阵补全和不完全RPCA等方法在恢复丢失元素和分离前景上具有优越性。

Because the existing Robust Principal Component Analysis （RPCA） approaches do not consider the continuity and the incompletion of sequential data, one type of low-rank matrix recovery model, named Regularized Incomplete RPCA （RIRPCA）, was proposed. First, the model of RIRPCA was constructed based on a metric function for evaluating the continuity, where the model minimized a weighted combination of the matrix nuclear norm, L1 norm and regularized term. Then, the augmented Lagrange multipliers algorithm was employed to solve the proposed convex optimization problem. This algorithm has good scalability and low computation complexity, Finally, RIRPCA was applied to the background modeling of videos. The experimental results demonstrate that the proposed method has the superiority of recovering missing entries and separating foreground over matrix completion and incomplete RPCA.