Low Rank Prior and Total Variation Regularization for Image Deblurring |
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Authors: | Liyan Ma Li Xu Tieyong Zeng |
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Affiliation: | 1.Institute of Microelectronics of Chinese Academy of Sciences,Beijing,China;2.LSEC, Institute of Computational Mathematics, Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing,China;3.Department of Mathematics,Hong Kong Baptist University,Kowloon Tong,Hong Kong;4.HKBU Institute of Research and Continuing Education,Shenzhen,China |
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Abstract: | The similar image patches should have similar underlying structures. Thus the matrix constructed from stacking the similar patches together has low rank. Based on this fact, the nuclear norm minimization, which is the convex relaxation of low rank minimization, leads to good denoising results. Recently, the weighted nuclear norm minimization has been applied to image denoising. This approach presents state-of-the-art result for image denoising. In this paper, we further study the weighted nuclear norm minimization problem for general image recovery task. For the weights being in arbitrary order, we prove that such minimization problem has a unique global optimal solution in the closed form. Incorporating this idea with the celebrated total variation regularization, we then investigate the image deblurring problem. Numerical experimental results illustratively clearly that the proposed algorithms achieve competitive performance. |
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