Robust Tensor Principal Component Analysis in All Modes

Longxi Chen, Yipeng Liu, Ce Zhu

Abstract: Robust tensor principal component analysis extracts the low rank and sparse component of multi-dimensional data by tensor singular value decomposition (t-SVD), which can be used for many data analysis problems. However, the current t-SVD based methods cannot fully extract the low rank component in tensor data, and low rank structure still exists in the core tensor, because t-SVD does not decompose data in the third mode. To fully exploit the low rank structure, we further extract the low rank component using low rank plus sparsity for the core matrix whose entries are from the diagonal elements of the frontal slices in the core tensor. The proposed method is applied to three groups of numerical experiments on image denoising, illumination normalization for face images and motion separation for surveillance videos, respectively, and the results show that the proposed method outperforms state-of-the-art methods in terms of both accuracy and computational complexity.