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Image diffusion filtering algorithm combined with variable exponent and convective constraint

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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.

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References

  1. Krissian, K., Westin, C.F., Kikinis, R.: Oriented speckle reducing anisotropic diffusion. IEEE Trans. Image Process. 16(5), 1412–1424 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  2. Ghimpeteanu, G., Batard, T., Bertalmio, M.: A decomposition framework for image denoising algorithms. IEEE Trans. Image Process. 25(1), 388–399 (2016)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  8. You, Y., Kaveh, M.: Fourth-order partial differential equations for noise removal. IEEE Trans. Image Process. 9(10), 1723–1730 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  12. Yu, J., Tan, J., Wang, Y.: Ultrasound speckle reduction by a SUSAN-controlled anisotropic diffusion method. Pattern Recognit. 43(9), 3083–3092 (2010)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  14. Hajiaboli, M.R.: An anisotropic fourth-order diffusion filter for image noise removal. Int. J. Comput. Vis. 92, 177–191 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  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. You, Y.L., Wen, Y.X.: Behavioral analysis of anisotropic diffusion in image processing. IEEE Trans. Image Process. 5(11), 1539–1552 (1996)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  18. Elad, M., Aharon, M.: Image denoising via sparse and redundant representations over learned dictionaries. IEEE Trans. Image Process. 15(12), 3736–3745 (2006)

    Article  MathSciNet  Google Scholar 

  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. 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)

    Article  Google Scholar 

  21. Liu, X.: Efficient algorithms for hybrid regularizers based image denoising and deblurring. Comput. Math. Appl. 69, 675–687 (2015)

    Article  MathSciNet  Google Scholar 

  22. Baloch, G., Ozkaramanli, H.: Image denoising via correlation-based sparse representation. Signal Image Video Process. 11(8), 1501–1508 (2017)

    Article  Google Scholar 

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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.

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Authors and Affiliations

  1. School of Mathematics and Computer Sciences, Shangrao Normal University, Shangrao, 334001, China

    Jinhua Liu & Yongming Li

  2. School of Physics and Electronic Information, Shangrao Normal University, Shangrao, 334001, China

    Qiu Tu

  3. School of Information and Software Engineering, University of Electronic Science and Technology of China, Chengdu, 610054, China

    Kun She

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  1. Jinhua Liu
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  2. Kun She
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Correspondence to Jinhua Liu.

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Liu, J., She, K., Li, Y. et al. Image diffusion filtering algorithm combined with variable exponent and convective constraint. SIViP 13, 87–94 (2019). https://doi.org/10.1007/s11760-018-1331-8

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  • DOI: https://doi.org/10.1007/s11760-018-1331-8

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