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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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References

  1. Burger, W., Burge, M.J.: Digital Image Processing. Texts in Computer Science. Springer, London (2008)

    Book  Google Scholar 

  2. Hwang, H., Haddad, Richard A.: Adaptive median filters new algorithms and results. IEEE Trans. Image Process. 4(4), 499–502 (1995)

    Article  Google Scholar 

  3. Ibrahim, H., Kong, N.S.P., Ng, T.F.: Simple adaptive median filter for the removal of impulse noise from highly corrupted images. IEEE Trans. Consum. Electron. 54(4), 1920–1927 (2008)

    Article  Google Scholar 

  4. Wang, Z., Zhang, D.: Progressive switching median filter for the removal of impulse noise from highly corrupted images. IEEE Trans. Circuits Syst. II 46(1), 78–80 (1999)

    Article  Google Scholar 

  5. Sun, T., Neuvo, Y.: Detail-preserving median based filters in image processing. Pattern Recognit. Lett. 15(4), 341–347 (1994)

    Article  Google Scholar 

  6. Hsieh, M.-H., Cheng, F.-C., Shie, M.-C., Ruan, S.-J.: Fast and efficient median filter for removing 1–99% levels of salt-and-pepper noise in images. Eng. Appl. Artif. Intell. 26(4), 1333–1338 (2012)

    Article  Google Scholar 

  7. Srinivasan, K.S., Ebenezer, D.: A new fast and efficient decision-based algorithm for removal of high-density impulse noises. Signal Process. Lett. IEEE. 14(3), 189–192 (2007)

    Article  Google Scholar 

  8. Esakkirajan, S., Veerakumar, T., Subramanyam, Adabala N., PremChand, C.H.: Removal of high density salt and pepper noise through modified decision based unsymmetric trimmed median filter. Signal Process. Lett. IEEE 18(5), 287–290 (2011)

    Article  Google Scholar 

  9. Aiswarya, K., Jayaraj, V., Ebenezer, D.: A new and efficient algorithm for the removal of high density salt-and-pepper noise in images and videos. ICCMS’10. Second International Conference on Computer Modeling and Simulation, 2010. vol. 4, pp. 409–413. (2010)

  10. Lu, C., Chou, T.: Denoising of salt-and-pepper noise corrupted image using modified directional-weighted-median filter. Elsevier Pattern Recognit. Lett. 33, 1287–1295 (2012)

    Article  Google Scholar 

  11. Wang, S.S., Wu, C.H.: A new impulse detection and filtering method for removal of wide range impulse noises. Pattern Recognit. 42(9), 2194–2202 (2009)

    Article  MATH  Google Scholar 

  12. Chan, R.H., Ho, C.W., Nikolova, M.: Salt-and-pepper noise removal by median-type noise detector and edge-preserving regularization. IEEE Trans. Image Process. 14, 1479–1485 (2005)

    Article  Google Scholar 

  13. Chen, S., Yang, X., Cao, G.: Impulse noise suppression with an augmentation of ordered difference noise detector and an adaptive variational method. Pattern Recognit. Lett. 30, 460–467 (2009)

    Article  Google Scholar 

  14. Jung, M., Vese, L.A.: Nonlocal variational image deblurring models in the presence of Gaussian or impulse noise. Scale Space and Variational Methods in Computer Vision, 401–412(2009)

  15. Nikolova, M.: A variational approach to remove outliers and impulse noise. J. Math. Imaging Vis. 20, 99–120 (2004)

    Article  MathSciNet  Google Scholar 

  16. Cai, J.F., Chan, R.H., Di Fiore, C.: Minimization of a detail-preserving regularization functional for impulse noise removal. J. Math. Imaging Vis. 29(1), 79–91 (2007)

    Article  Google Scholar 

  17. Buades, A., Coll, B., Morel, J.M.: On image denoising method. Technical report, CMLA Preprint 5 (2004)

  18. Awate, S.P., Whitaker, R.T.: Unsupervised, information-theoretic, adaptive image filtering for image restoration. IEEE Trans. Pattern Anal. Mach. Intell. 28(3), 364–376 (2006)

    Article  Google Scholar 

  19. Brox, T., Kleinschmidt, O., Cremers, D.: Efficient nonlocal means for denoising of textural patterns. IEEE Trans. Image Process. 17(7), 1083–1092 (July 2008)

  20. Protter, M., Elad, M.: Image sequence denoising via spare and redundant representations. IEEE Trans. Image Process. 18(1), 27–35 (2009)

    Article  MathSciNet  Google Scholar 

  21. Gilboa, G., Osher, S.: Nonlocal operators with applications to image processing. Multiscale Modeling Simul. 7(3), 1005–1028 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  22. Chan, R. H., Ho, C. W., Leung, C. Y., Nikolova, M.: Minimization of detail-preserving regularization functional by Newtons method with continuation. In: Proceedings of IEEE International Conference on Image Processing, pp. 125–128. (2005)

  23. Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 12(7), 629–639 (Jul 1990)

  24. Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13(4), 600–612 (2004)

    Article  Google Scholar 

  25. Cai, J.-F., Chan, R., Nikolova, M.: Fast two-phase image deblurring under impulse noise. J. Math. Imaging Vis. 36, 46–53 (Apr 2010)

  26. Luminita, V.: A study in the bv space of a denoisingdeblurring variational problem. Appl. Math. Optim. 44(2), 131–161 (2001)

    Article  MathSciNet  Google Scholar 

  27. Rudin, L., Osher, S.: Nonlinear total variation based noise removal algorithms. Physica D 60, 259–268 (1992)

    Article  MATH  Google Scholar 

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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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  4. Jiebao Sun
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  5. Dazhi Zhang
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  6. Boying Wu
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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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