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Multiscale Decomposition in Low-Rank Approximation
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DOI：10.1109/LSP.2017.2704024.png)
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Abstract
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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.
Keywords:
Low-rank approximation
multiscale representation
nonlinear optimization
nuclear norm
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