Iterative Block Tensor Singular Value Thresholding for Extraction of Low Rank Component of Image Data
This work addresses the problem of robust tensor PCA for applications like video and image analysis, but it appears incremental as it builds on existing tensor decomposition methods with a block-based approach.
The paper tackles the problem of extracting principal components from multi-way data by proposing a robust tensor PCA method that splits tensors into blocks and applies iterative singular value thresholding to each block, then concatenates the low-rank components. The method is demonstrated to be effective in motion separation for surveillance videos and illumination normalization for face images, though no concrete numbers are provided in the abstract.
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 princi- pal 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 prin- cipal 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 decom- position. This factorization has similar optimality properties to that of low rank matrix derived from singular value decomposition. Ex- perimentally, we demonstrate its effectiveness in two applications, including motion separation for surveillance videos and illumination normalization for face images.