Iterative block tensor singular value thresholding for extraction of lowrank component of image data

Tensor principal component analysis (TPCA) is a multi-linear extension of principal component analysis which converts a set of correlated measurements into several principal components. In this paper, we propose a new robust TPCA method to extract the principal components of the multi-way data based on tensor singular value decomposition. The tensor is split into a number of blocks of the same size. The low rank component of each block tensor is extracted using iterative tensor singular value thresholding method. The principal components of the multi-way data are the concatenation of all the low rank components of all the block tensors. We give the block tensor incoherence conditions to guarantee the successful decomposition. This factorization has similar optimality properties to that of low rank matrix derived from singular value decomposition. Experimentally, we demonstrate its effectiveness in two applications, including motion separation for surveillance videos and illumination normalization for face images.