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Blind image deblurring via L1-regularized second-order gradient prior

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Abstract

The blind image deblurring is to find the underlying true image and the blur kernel from a blurred observation. This is a well-known ill-conditional problem in image processing field. To obtain a pleasant deblurred result, additional assumptions and prior knowledge are required. Proposed in this work is a simple and efficient blind image deblurring method which utilizes L1-regularized second-order gradient prior. The inspiration for this work comes from the fact that the absolute values of the second-order gradient elements decrease with motion blur. This change is an essential feature of the motion blur process, and we demonstrate it mathematically in this paper. By enforcing the L1 norm constraint to the term involving second-order gradients and incorporating it into the traditional deblurring framework, an effective optimization scheme is explored. The half-quadratic splitting technique is adopted to handle the non-convex minimum problem. Experimental results illustrate that our algorithm outperforms the state-of-art image deblurring algorithms in both benchmark datasets and ground-truth scenes. Besides, this algorithm is simple since it does not require any heuristic edge selection steps or involves too many nonlinear operators.

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Acknowledgements

We would like to thank the reviewers for their helpful comments and suggestions which greatly improve the quality of the paper. This work was supported by the National Natural Science Foundation of China under Grant 62172135.

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Authors and Affiliations

  1. School of Computer and Information, Hefei University of Technology, Hefei, 230009, People’s Republic of China

    Jing Liu, Jieqing Tan & Xianyu Ge

  2. School of Mathematics, Hefei University of Technology, Hefei, 230009, People’s Republic of China

    Li Zhang

  3. Nanjing Marine Radar Institute, Nanjing, 210000, People’s Republic of China

    Xingchen Zhu

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  1. Jing Liu
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  2. Jieqing Tan
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  3. Li Zhang
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Correspondence to Jieqing Tan.

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Liu, J., Tan, J., Zhang, L. et al. Blind image deblurring via L1-regularized second-order gradient prior. Multimed Tools Appl 81, 39121–39144 (2022). https://doi.org/10.1007/s11042-022-13010-y

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