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Adaptive Nonconvex Nonsmooth Regularization for Image Restoration Based on Spatial Information

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Abstract

Image restoration is an ill-posed problem that requires regularization to solve. Many existing regularization terms in the literature are the convex function. However, nonconvex nonsmooth regularization has advantages over convex regularization for restoring images, but its practical interest used to be limited by the difficulty of the computational stage which requires a nonconvex nonsmooth minimization. In this paper, an adaptive nonconvex nonsmooth regularization is proposed for image restoration by using the spatial information indicator. Moreover, an efficient numerical algorithm for solving the resulting minimization problem is provided by applying the variable splitting and the penalty techniques. Finally, its advantages are shown in deblurring edges and restoring fines of image simultaneously in experiments.

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Acknowledgments

The authors would like to thank the editors and the anonymous reviewers for their valuable suggestions. We also would like to thank Anmin Liu, Houzhang Fang, and Professor Mila Nikolova for supplying the Matlab implementation of their algorithm. This work was supported by the Project of the key National Natural Science Foundation of China under Grant No. 60736010, No. 60902060, No. 61227007, Innovation Research Fund Committee of HUST (2011QN073), and Innovation Fund of CASC (CASC 201104).

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Authors and Affiliations

  1. Institute for Pattern Recognition and Artificial Intelligence, Huazhong University of Science and Technology, Wuhan, 430074, China

    Zhiyong Zuo, WeiDong Yang, Li Liu, Jing Hu & Luxin Yan

  2. The 10th Institute of China Electronics Technology Group Corporation, Chengdu, 610036, China

    Zhiyong Zuo & Xia Lan

  3. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China

    Xia Lan

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  1. Zhiyong Zuo
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  2. WeiDong Yang
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  3. Xia Lan
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  4. Li Liu
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  6. Luxin Yan
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Correspondence to Zhiyong Zuo.

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Zuo, Z., Yang, W., Lan, X. et al. Adaptive Nonconvex Nonsmooth Regularization for Image Restoration Based on Spatial Information. Circuits Syst Signal Process 33, 2549–2564 (2014). https://doi.org/10.1007/s00034-014-9760-2

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  • DOI: https://doi.org/10.1007/s00034-014-9760-2

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