Advertisement

Image diffusion filtering algorithm combined with variable exponent and convective constraint

  • Jinhua Liu
  • Kun She
  • Yongming Li
  • Qiu Tu
Original Paper
  • 60 Downloads

Abstract

A diffusion function based on mixed gradient and variable exponent is built by combining image characteristics in wavelet transform and spatial domains to solve the edge blurring problem of the traditional anisotropic diffusion model in image filtering and improve image filtering performance. A convective term is introduced as a constraint in the image diffusion model to control the strength of image diffusion, and an image adaptive diffusion filtering algorithm is developed. Experimental simulation using test images as research objects is performed to verify the effectiveness of the proposed algorithm. Results show that the proposed algorithm effectively inhibits the edge blurring effect during image diffusion and improves the visual quality of the filtered image.

Keywords

Image filtering Diffusion model Convective constraint Variable exponent Structural similarity 

Notes

Acknowledgements

This work was supported by the Science and Technology Foundation of Jiangxi Provincial Education Department (No. GJJ170922) and the National Natural Science Foundation of China under No. 11461057.

References

  1. 1.
    Krissian, K., Westin, C.F., Kikinis, R.: Oriented speckle reducing anisotropic diffusion. IEEE Trans. Image Process. 16(5), 1412–1424 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Ghimpeteanu, G., Batard, T., Bertalmio, M.: A decomposition framework for image denoising algorithms. IEEE Trans. Image Process. 25(1), 388–399 (2016)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Storath, M., Brandt, C., Hofmann, M., Salamon, J., Weber, A., Weinmann, A.: Edge preserving and noise reducing reconstruction for magnetic particle imaging. IEEE Trans. Med. Imaging 36(1), 74–85 (2017)CrossRefGoogle Scholar
  4. 4.
    Zhang, J.C., Hirakawa, K.: Improved denoising via poisson mixture modeling of image sensor noise. IEEE Trans. Image Process. 26(4), 1565–1578 (2017)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Wen, B.H., Ravishankar, S., Bresler, Y.: Structured overcomplete sparsifying transform learning with convergence guarantees and applications. Int. J. Comput. Vis. 114, 137–167 (2015)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 12(7), 629–639 (1990)CrossRefGoogle Scholar
  7. 7.
    Catte, F., Lions, P.L., Morel, J.M., Tomel, C.: Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. Numer. Anal. 29(1), 182–193 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    You, Y., Kaveh, M.: Fourth-order partial differential equations for noise removal. IEEE Trans. Image Process. 9(10), 1723–1730 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Gilboa, G., Sochen, N., Zeevi, Y.: Forward-and backward diffusion processes for adaptive image enhancement and denoising. IEEE Trans. Image Process. 11(7), 689–703 (2002)CrossRefGoogle Scholar
  10. 10.
    Gilboa, G., Sochen, N., Zeevi, Y.Y.: Image enhancement and denoising by complex diffusion process. IEEE Trans. Pattern Anal. Mach. Intell. 26(8), 1020–1036 (2004)CrossRefGoogle Scholar
  11. 11.
    Yu, J.H., Wang, Y.Y., Shen, Y.Z.: Noise reduction and edge detection via kernel anisotropic diffusion. Pattern Recognit. Lett. 29(10), 1496–1503 (2008)CrossRefGoogle Scholar
  12. 12.
    Yu, J., Tan, J., Wang, Y.: Ultrasound speckle reduction by a SUSAN-controlled anisotropic diffusion method. Pattern Recognit. 43(9), 3083–3092 (2010)CrossRefGoogle Scholar
  13. 13.
    Guo, Z.C., Sun, J.B., Zhang, D.Z., Wu, B.Y.: Adaptive Perona–Malik model based on the variable exponent for image denoising. IEEE Trans. Image Process. 21(3), 958–967 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Hajiaboli, M.R.: An anisotropic fourth-order diffusion filter for image noise removal. Int. J. Comput. Vis. 92, 177–191 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Liu, J.H., She, K.: Image diffusion filtering based on dual tree complex wavelet and wave atoms. Acta Physica Sinica 60(12), 124203-1-10 (2011)Google Scholar
  16. 16.
    You, Y.L., Wen, Y.X.: Behavioral analysis of anisotropic diffusion in image processing. IEEE Trans. Image Process. 5(11), 1539–1552 (1996)CrossRefGoogle Scholar
  17. 17.
    Wang, Z., Bovika, A.C., Sheikh, H.R., Simoncellie, P.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13(4), 600–612 (2004)CrossRefGoogle Scholar
  18. 18.
    Elad, M., Aharon, M.: Image denoising via sparse and redundant representations over learned dictionaries. IEEE Trans. Image Process. 15(12), 3736–3745 (2006)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Dabov, K., Foi, A., Katkovnik, V., Egiazarian, K.: BM3D image denoising with shape-adaptive principal component analysis. In: Proc. Workshop on Signal Processing with Adaptive Sparse Structured Representations (SPARS’09), Saint-Malo (2009). https://www.cs.tut.fi/~foi/papers/SPARS09-BM3D-SAPCA.pdf
  20. 20.
    Yang, M., Liang, J., Zhang, J., Gao, H., Meng, F., Li, X., Song, S.: Non-local means theory based Perona–Malik model for image denoising. Neurocomputing 2013(120), 262–267 (2013)CrossRefGoogle Scholar
  21. 21.
    Liu, X.: Efficient algorithms for hybrid regularizers based image denoising and deblurring. Comput. Math. Appl. 69, 675–687 (2015)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Baloch, G., Ozkaramanli, H.: Image denoising via correlation-based sparse representation. Signal Image Video Process. 11(8), 1501–1508 (2017)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and Computer SciencesShangrao Normal UniversityShangraoChina
  2. 2.School of Physics and Electronic InformationShangrao Normal UniversityShangraoChina
  3. 3.School of Information and Software EngineeringUniversity of Electronic Science and Technology of ChinaChengduChina

Personalised recommendations