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Adapting total generalized variation for blind image restoration

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Abstract

In this paper, a fast blind deconvolution approach is proposed for image deblurring by modifying a recent well-known natural image model, i.e., the total generalized variation (TGV). As a generalization of total variation, TGV aims at reconstructing a higher-quality image with high-order smoothness as well as sharp edge structures. However, when it turns to the blind issue, as demonstrated either empirically or theoretically by several previous blind deblurring works, natural image models including TGV actually prefer the blurred images rather than their counterpart sharp ones. Inspired by the discovery, a simple, yet effective modification strategy is applied to the second-order TGV, resulting in a novel L0–L1-norm-based image regularization adaptable to the blind deblurring problem. Then, a fast numerical scheme is deduced with O(NlogN) complexity for alternatingly estimating the intermediate sharp images and blur kernels via coupling operator splitting, augmented Lagrangian and also fast Fourier transform. Experiment results on a benchmark dataset and real-world blurred images demonstrate the superiority or comparable performance of the proposed approach to state-of-the-art ones, in terms of both deblurring quality and speed. Another contribution in this paper is the application of the newly proposed image prior to single image nonparametric blind super-resolution, which is a fairly more challenging inverse imaging task than blind deblurring. In spite of that, we have shown that both blind deblurring and blind super-resolution (SR) can be formulated into a common regularization framework. Experimental results demonstrate well the feasibility and effectiveness of the proposed blind SR approach, and also its advantage over the recent method by Michaeli and Irani in terms of estimation accuracy.

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Notes

  1. Since 20 March, 2013, the authors of (Xu et al. 2013) have successively released two executable software (implemented in C ++) for blind motion deblurring, i.e., Robust Motion Deblurring System. The first version is v3.0.1 which implements the algorithm as detailed in Xu et al. (2013), and the second version is v3.1 which incorporates the algorithms in both Xu et al. (2013) and Dong et al. (2014), i.e. Xu et al. (2013), Dong et al. (2014), for more accurate blur-kernel estimation.

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Acknowledgements

Many thanks are given to the anonymous reviewers for their pertinent and helpful comments which have improved the paper a lot. The first author is very grateful to Prof. Zhi-Hui Wei, Prof. Yi-Zhong Ma, Dr. Min Wu, and Mr. Ya-Tao Zhang for their kind supports in the past years. The study was supported in part by the Natural Science Foundation (NSF) of China (61771250, 61402239, 61602257, 11671004), NSF of Jiangsu Province (BK20130868, BK20160904) and Guangxi Provinces (2014GXNSFAA118360), NSF for the Jiangsu Institutions (16KJB520035), and also the Open Project Fund of both Jiangsu Key Laboratory of Image and Video Understanding for Social Safety (Nanjing University of Science and Technology, 30920140122007) and National Engineering Research Center of Communications and Networking (Nanjing University of Posts and Telecommunications, TXKY17008).

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Authors and Affiliations

  1. College of Telecommunications and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing, China

    Wen-Ze Shao & Feng Wang

  2. National Engineering Research Center of Communications and Networking, Nanjing University of Posts and Telecommunications, Nanjing, China

    Wen-Ze Shao

  3. Jiangsu Key Laboratory of Image and Video Understanding for Social Safety, Nanjing University of Science and Technology, Nanjing, China

    Wen-Ze Shao

  4. Institutes of Advanced Technology, Zhejiang Dahua Technology Co., Ltd., Hangzhou, China

    Feng Wang

  5. School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing, China

    Li-Li Huang

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  1. Wen-Ze Shao
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Correspondence to Wen-Ze Shao.

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Shao, WZ., Wang, F. & Huang, LL. Adapting total generalized variation for blind image restoration. Multidim Syst Sign Process 30, 857–883 (2019). https://doi.org/10.1007/s11045-018-0586-0

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