Skip to main content
SpringerLink
Log in

Studying the influence of search rule and context shape in filtering impulse noise images with Markov chains

  • Original Paper
  • Published:
Signal, Image and Video Processing Aims and scope Submit manuscript

Abstract

The paper presents an improved context-based denoising method for gray scale images affected by impulse noise. The proposed algorithm is using Markov chains to replace the detected noise with the intensity having the highest number of occurrences in similar contexts. The context of a noisy pixel consists in its neighbor pixels and is searched in a larger but limited surrounding area. We have analyzed different search methods and different context shapes. The experimental results obtained on the test images have shown that the most efficient model applies the search in form of   “*”  of contexts in form of   “+”. Besides the better denoising performance obtained on all the noise levels, the computational time has been also significantly improved with respect to our previous context-based filter which applied full search of full context. We have also compared this improved Markov filter with other denoising techniques existing in the literature, most of them being significantly outperformed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Gellert, A., Brad, R.: Context-based prediction filtering of impulse noise images. IET Image Process. 10(6), 429–437 (2016)

    Article  Google Scholar 

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

    Article  Google Scholar 

  3. Hamza, A.B., Luque-Escamilla, P., Martínez-Aroza, J., Román-Roldán, R.: Removing noise and preserving details with relaxed median filters. J. Math. Imaging Vis. 11(2), 161–177 (1999)

    Article  MathSciNet  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 Analog Dig. Signal Process. 46(1), 78–80 (1999)

    Article  MathSciNet  Google Scholar 

  5. Toh, K.K.V., Isa, N.A.M.: Noise adaptive fuzzy switching median filter for salt-and-pepper noise reduction. IEEE Signal Process. Lett. 17(3), 281–284 (2010)

    Article  Google Scholar 

  6. Chan, R.H., Ho, C.-W., Nikolova, M.: Convergence of Newton’s method for a minimization problem in impulse noise removal. J. Comput. Math. 22(2), 168–177 (2004)

    MathSciNet  MATH  Google Scholar 

  7. Chan, R.H., Ho, C.-W., Nikolova, M.: Salt-and-pepper noise removal by median-type noise detectors and detail-preserving regularization. IEEE Trans. Image Process. 14(10), 1479–1485 (2005)

    Article  Google Scholar 

  8. Xu, Z., Wu, H.R., Yu, X., Qiu, B.: Adaptive progressive filter to remove impulse noise in highly corrupted color images. Signal Image Video Process. 7(5), 817–831 (2013)

    Article  Google Scholar 

  9. Nasri, M., Saryazdi, S., Nezamabadi-pour, H.: A fast adaptive salt and pepper noise reduction method in images. Circuits Syst. Signal Process. 32(4), 1839–1857 (2013)

    Article  Google Scholar 

  10. Krejcar, O., Frischer, R.: Non destructive defect detection by spectral density analysis. Sensors 11(3), 2334–2346 (2011)

    Article  Google Scholar 

  11. Estrada, F., Fleet, D., Jepson, A.: Stochastic image denoising. British Machine Vision Conference, London, p. 117 (2009)

  12. Wong, A., Mishra, A., Zhang, W., Fieguth, P., Clausi, D.A.: Stochastic image denoising based on Markov-Chain Monte Carlo sampling. Signal Process. 91(8), 2112–2120 (2011)

    Article  MATH  Google Scholar 

  13. Berkovich, H., Malah, D., Barzohar, M.: Non-local means denoising using a content-based search region and dissimilarity kernel. In: 8th International Symposium on Image and Signal Processing and Analysis (ISPA), Trieste, pp. 10–15 (2013)

  14. Mishra, B.K., Bharadi, V.A., Nemade, B., Thakur, K.V., Damodare, O.H., Sapkal, A.M.: Poisson noise reducing bilateral filter. In: Proceedings of International Conference on Communication, Computing and Virtualization (ICCCV) 2016, Procedia Computer Science, vol. 79, pp. 861–865 (2016)

  15. Smolka, B., Kusnik, D.: Robust local similarity filter for the reduction of mixed Gaussian and impulsive noise in color digital images. Signal Image Video Process. 9(1), 49–56 (2015)

    Article  Google Scholar 

  16. Rouf, M., Ward, R.K.: Retrieving information lost by image denoising. In: 2015 IEEE Global Conference on Signal and Information Processing (GlobalSIP), Orlando, FL, pp. 1066–1070 (2015)

  17. Horng, S.J., Hsu, L.Y., Li, T., Qiao, S., Gong, X., Chou, H.H., Khan, M.K.: Using sorted switching median filter to remove high-density impulse noises. J. Vis. Commun. Image Represent. 24(7), 956–967 (2013)

    Article  Google Scholar 

  18. Liu, L., Chen, C.P., Zhou, Y., You, X.: A new weighted mean filter with a two-phase detector for removing impulse noise. Inf. Sci. 315, 1–16 (2015)

    Article  MathSciNet  Google Scholar 

  19. Bingham, E., Mannila, H.: Random projection in dimensionality reduction: applications to image and text data. In: 7th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, USA, pp. 245–250 (2001)

  20. Jääskinen, V., Parkkinen, V., Cheng, L., Corander, J.: Bayesian clustering of DNA sequences using Markov chains and a stochastic partition model. Stat. Appl. Genet. Mol. Biol. 13(1), 105–121 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  21. Gellert, A., Florea, A.: Web prefetching through efficient prediction by partial matching. World Wide Web Internet Web Inf. Syst. 19(5), 921–932 (2016). doi:10.1007/s11280-015-0367-8

    Article  Google Scholar 

  22. Gambs, S., Killijian, M.O., del Prado Cortez, M.N.: Next place prediction using mobility markov chains. In: Proceedings of the First Workshop on Measurement, Privacy, and Mobility, New York, USA, p. 3 (2012)

  23. Waghchawre, A.J., Shinde, J.V.: Query mining for image retrieval system using Markov chain model. In: International Conference on Emerging Trends in Computer Engineering, Science and Information Technology, India, pp. 109–112 (2015)

  24. Mushtaq, A., Lee, C.-H.: An integrated approach to feature compensation combining particle filters and hidden Markov model for robust speech recognition. In: IEEE International Conference on Acoustics, Speech, and Signal Processing, Kyoto, Japan, pp. 4757–4760 (2012)

  25. Rabiner, L.R.: A tutorial on hidden Markov models and selected applications in speech recognition. Proc. IEEE 77(2), 257–286 (1989)

    Article  Google Scholar 

  26. Gellert, A., Florea, A.: Investigating a new design pattern for efficient implementation of prediction algorithms. J. Dig. Inf. Manag. 11(5), 366–377 (2013)

    Google Scholar 

  27. Majumdar, A., Ward, R.K.: Synthesis and analysis prior algorithms for joint-sparse recovery. In: IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 3421–3424 (2012)

Download references

Author information

Authors and Affiliations

  1. Computer Science and Electrical Engineering Department, Lucian Blaga University of Sibiu, Emil Cioran Street, No. 4, 550025, Sibiu, Romania

    Arpad Gellert & Remus Brad

Authors
  1. Arpad Gellert
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Remus Brad
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Arpad Gellert.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (doc 7773 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gellert, A., Brad, R. Studying the influence of search rule and context shape in filtering impulse noise images with Markov chains. SIViP 12, 315–322 (2018). https://doi.org/10.1007/s11760-017-1160-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11760-017-1160-1

Keywords

Search

Navigation