Multiscale Decomposition in Low-Rank Approximation

In low-rank approximation methods, it is often assumed that the data matrix is composed of two globally low-rank and sparse matrices. Moreover, real data matrices often consist of local patterns in multiple scales. The conventional low-rank approximation techniques do not reveal the local patterns from the data matrices. This letter presents an approach based on decomposition of matrices into low-rank components in different scales. We propose a novel framework using image pyramids comprises of two steps: first locating and then extracting low-rank patterns in multiple scales using nonlinear optimization. Experimentally, we show that the proposed approach is more efficient in extracting low-rank patterns in challenging tasks of illumination normalization in face images and background subtraction in video data.