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Salt-and-Pepper Noise Removal via Local Hölder Seminorm and Nonlocal Operator for Natural and Texture Image

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Abstract

Utilizing local Hölder seminorm and nonlocal operator, we propose two efficient salt-and-pepper noise removal algorithms in this paper. We first minimize a local Hölder seminorm based functional which has a great capacity to restore natural images. Then by the definition of nonlocal operator, a new TV-based functional is proposed which inherits the advantage of nonlocal method and not only suppresses the noise but also restores the geometrical and texture features of noisy images. An alternative numerical scheme is also proposed to solve our functionals which reduces the computational complexity greatly. Experimental results are reported to compare the existing methods and demonstrate that the proposed algorithms are efficient even when the noise level is as high as 90 %.

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Acknowledgments

The authors wish to thank the referee for careful reading of the early version of this manuscript and proving valuable suggestions and comments. The author would also like to thank Raymond Chan from the Chinese University of Hong Kong for providing the source code of TPM. This work is partially supported by the National Science Foundation of China (11271100 and 11301113), the Ph.D. Programs Foundation of Ministry of Education of China (no. 20132302120057), the class General Financial Grant from the China Postdoctoral Science Foundation (Grant no. 2012M510933), the Fundamental Research Funds for the Central Universities (Grant nos. HIT. NSRIF. 2011003 and HIT. A. 201412), the Program for Innovation Research of Science in Harbin Institute of Technology (Grant no. PIRS OF HIT A201403), and Harbin Science and Technology Innovative Talents Project of Special Fund (2013RFXYJ044).

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Authors and Affiliations

  1. Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, People’s Republic of China

    Kehan Shi, Zhichang Guo, Gang Dong, Jiebao Sun, Dazhi Zhang & Boying Wu

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  1. Kehan Shi
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  2. Zhichang Guo
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  3. Gang Dong
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Correspondence to Zhichang Guo.

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Shi, K., Guo, Z., Dong, G. et al. Salt-and-Pepper Noise Removal via Local Hölder Seminorm and Nonlocal Operator for Natural and Texture Image. J Math Imaging Vis 51, 400–412 (2015). https://doi.org/10.1007/s10851-014-0531-2

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