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3D Filtering of Images Corrupted by Additive-Multiplicative Noise

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Abstract

A novel method for filtering images contaminated by mixed (additive-multiplicative) noise is substantiated and implemented for the first time. The method includes several stages: the formation of similar structures in 3D space, homomorphic transformation, a 3D filtering approach based on a sparse representation in the discrete cosine transform space, inverse homomorphic transformation, and final post-processing that involves bilateral filtering and the reconstruction of edges and details. A physical interpretation of the filtering procedure under mixed noise conditions is given, and a filtering block diagram is developed. Numerous experiments based on the developed method have confirmed its superiority in term of conventional criteria, such as the structural similarity index measure and the peak signal-to-noise ratio, as well as in term of visual image quality via human perception.

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REFERENCES

  1. D. Guan, D. Xiang, X. Tang, and G. Kuang, IEEE Trans. GeoSci. Rem. Sens. 57 (6), 3472–3489 (2018).

    Article  Google Scholar 

  2. T. Huang, W. Dong, X. Xie, G. Shi, and X. Bai, IEEE Trans. Image Process. 26 (7), 3171–3186 (2017).

    Article  MathSciNet  Google Scholar 

  3. O. Rubel, V. Lukin, and K. Egiazarian, Elect. Imaging 2019 (11), 1–11 (2019).

    Google Scholar 

  4. G. Wang, Z. Pan, and Z. Zhang, Multimedia Tools Appl. 78 (20), 29 007–29 019 (2019).

  5. S. V. M. Sagheer, S. N. George, and S. K. Kurien, Biomed. Signal Process. Cont. 54 (101595), 1–14 (2019).

    Google Scholar 

  6. V. F. Kravchenko, V. I. Ponomaryov, V. I. Pustovoit, and A. Palacios-Enriquez, Dokl. Phys. 62 (8), 379–383 (2017).

    Article  Google Scholar 

  7. V. F. Kravchenko, V. I. Ponomaryov, and V. I. Pustovoit, Dokl. Phys. 63 (8), 321–325 (2018).

    Article  Google Scholar 

  8. A. Palacios-Enriquez, V. Ponomaryov, R. Reyes-Reyes, and S. Sadovnychiy, Circuits Syst. Signal Process. 37 (12), 5389–5416 (2018).

    Article  Google Scholar 

  9. V. Ponomaryov, H. Montenegro, F. Gallegos, O. Pogrebnyak, and S. Sadovnychiy, Neurocomputing 155, 225–246 (2015).

    Article  Google Scholar 

  10. K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, IEEE Trans. Image Process. 16 (8), 2080–2095 (2007).

    Article  MathSciNet  Google Scholar 

  11. Y. Zhang, X. Tian, and P. Ren, Neurocomputing 140, 299–316 (2014).

    Article  Google Scholar 

  12. J. Jiang, L. Zhang, and J. Yang, IEEE Trans. Image Process. 23 (6), 2651–2662 (2014).

    Article  MathSciNet  Google Scholar 

  13. L. Malinski and B. Smolka, J. Real-Time Image Process. 11 (3), 427–444 (2016).

    Article  Google Scholar 

  14. Z. Wang and A. Bovik, IEEE Signal Process. Mag. 26 (1), 98–117 (2009).

    Article  Google Scholar 

  15. V. F. Kravchenko and O. V. Kravchenko, Constructive Methods of Algebra of Logic, Atomic Functions, Wavelets, and Fractals in Physics and Engineering, Ed. by V. F. Kravchenko (Tekhnosfera, Moscow, 2018) [in Russian].

    Google Scholar 

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Authors and Affiliations

  1. Kotelnikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences, 125009, Moscow, Russia

    V. F. Kravchenko

  2. Scientific and Technological Center of Unique Instrumentation, Russian Academy of Sciences, 117342, Moscow, Russia

    V. F. Kravchenko &  V. I. Pustovoit

  3. Bauman Moscow State Technical University, 105005, Moscow, Russia

    V. F. Kravchenko &  V. I. Pustovoit

  4. National Polytechnic Institute of Mexico, 04430, Mexico City, Mexico

    V. I. Ponomaryov & A. Palacios-Enriquez

Authors
  1. V. F. Kravchenko
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  2. V. I. Ponomaryov
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  3. V. I. Pustovoit
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  4. A. Palacios-Enriquez
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Corresponding authors

Correspondence to V. F. Kravchenko, V. I. Ponomaryov, V. I. Pustovoit or A. Palacios-Enriquez.

Additional information

Translated by I. Ruzanova

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Kravchenko, V.F., Ponomaryov, V.I., Pustovoit, V.I. et al. 3D Filtering of Images Corrupted by Additive-Multiplicative Noise. Dokl. Math. 102, 414–417 (2020). https://doi.org/10.1134/S1064562420050348

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  • DOI: https://doi.org/10.1134/S1064562420050348

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