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Linear total variation approximate regularized nuclear norm optimization for matrix completion. (English) Zbl 1474.94042

Summary: Matrix completion that estimates missing values in visual data is an important topic in computer vision. Most of the recent studies focused on the low rank matrix approximation via the nuclear norm. However, the visual data, such as images, is rich in texture which may not be well approximated by low rank constraint. In this paper, we propose a novel matrix completion method, which combines the nuclear norm with the local geometric regularizer to solve the problem of matrix completion for redundant texture images. And in this paper we mainly consider one of the most commonly graph regularized parameters: the total variation norm which is a widely used measure for enforcing intensity continuity and recovering a piecewise smooth image. The experimental results show that the encouraging results can be obtained by the proposed method on real texture images compared to the state-of-the-art methods.

MSC:

94A12 Signal theory (characterization, reconstruction, filtering, etc.)
15A83 Matrix completion problems
65K05 Numerical mathematical programming methods
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
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