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An Efficient Variational Method for Restoring Images with Combined Additive and Multiplicative Noise

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Abstract

This paper proposes a novel variational model to remove either independent additive or multiplicative noise from synthetic and natural digital images via the fractional-order derivative operator. The non-local characteristics of fractional derivatives can help preserve textures and eliminate the “blocky effect”. The proposed strategy uses the fractional-order total variation (FOTV)-norm, combined with the fields of experts-image prior model, a filter-based higher-order Markov Random Fields (MRF) method which is effective for image restoration. The present model combines advantages of both FOTV and higher order MRF and results in good restoration. In this study, a fast alternating minimization algorithm is also employed to solve minimization problem. Compared with the other well-established methods, experimental results show the effectiveness of the proposed method for de-noising images contaminated by combined additive and multiplicative noises. In addition, we also discuss parameter dependency and computational analysis in details.

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Acknowledgments

The work described in this paper was supported by the National Science Funds of China (Grant Nos. 11572111, 11372097) and the 111 Project (Grant No. B12032).

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Authors and Affiliations

  1. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Center for Numerical Simulation Software in Engineering and Sciences, College of Mechanics and Materials, Hohai University, Nanjing, Jiangsu, 210098, People’s Republic of China

    Asmat Ullah, Wen Chen, Mushtaq Ahmad Khan & HongGuang Sun

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  1. Asmat Ullah
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  2. Wen Chen
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  3. Mushtaq Ahmad Khan
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  4. HongGuang Sun
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Correspondence to Asmat Ullah or Wen Chen.

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Asmat Ullah, Chen, W., Khan, M.A. et al. An Efficient Variational Method for Restoring Images with Combined Additive and Multiplicative Noise. Int. J. Appl. Comput. Math 3, 1999–2019 (2017). https://doi.org/10.1007/s40819-016-0219-y

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