关键词: 鲁棒主成分分析, 高维数据, 低秩矩阵, 卷积鲁棒主成分分析, 乘子交替方向法

Abstract: Robust Principal Component Analysis (RPCA) is a classical high-dimensional data analysis method, which can recover original data from noisy observation samples. However, the premise that RPCA can work is that the target data has a low rank matrix structure, so that RPCA cannot effectively deal with non-low rank data in practical applications. It is found that the convolution matrices of image and video are usually low rank, although the data matrices of them may not be low rank. According to this principle, a new method called Convolution Robust Principal Component Analysis (CRPCA) was proposed to use the low rank property of convolution matrix to constrain the original data structure, so as to achieve accurate data recovery. The calculation process of CRPCA model is a convex optimization problem, which was solved by Alternating Direction Method of Multipliers (ADMM). Experimental results on synthetic data vectors, real data images and video sequences show that the proposed method is superior to other algorithms such as RPCA, Generalized Robust Principal Component Analysis (GRPCA) and Kernel Robust Principal Component Analysis (KRPCA) in dealing with non-low rank problems.

Key words: Robust Principal Component Analysis (RPCA), high-dimensional data, low rank matrix, Convolution Robust Principal Component Analysis (CRPCA), Alternating Direction Method of Multipliers (ADMM)