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An improved BM3D algorithm based on anisotropic diffusion equation

  • Received: 14 May 2020 Accepted: 14 July 2020 Published: 17 July 2020
  • Traditional 3D block matching (BM3D) algorithms are among the best denoising methods at present; however, they exhibit the issue of ringing around image edges, which makes them unable to protect image edges and details. Therefore, this paper proposes an BM3D noise processing algorithm for the diffusion equation to reduce image noise without affecting image details, specifically at the edges. This method first uses anisotropic diffusion (AD) filtering for image preprocessing, and then uses the edge direction instead of horizontal direction to search for similar blocks. The AD model is mainly improved to achieve better edges and detailed processing effects. Firstly, with the improved AD direction, a 5 × 5 edge enhancement operator model is implemented in eight directions, and the corresponding gradient information is obtained. This operator improves the processed image edges to achieve clear contours and good continuity. Next, a new calculation method for the diffusion function, whose coefficient is constructed using a hyperbolic tangent function, is introduced. The proposed method is based on the link between the image gradient and diffusion function, and it is mathematically proven that the diffusion function converges faster than the diffusion function of the model proposed by Perona and Malik. Experimental results indicate that the improved model can effectively retain the image edges and texture details, avoid edge ringing, and provide significant improvements in terms of the subjective visual effects and objective numerical indicators.

    Citation: Yanyan Zhang, Jingjing Sun. An improved BM3D algorithm based on anisotropic diffusion equation[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 4970-4989. doi: 10.3934/mbe.2020269

    Related Papers:

  • Traditional 3D block matching (BM3D) algorithms are among the best denoising methods at present; however, they exhibit the issue of ringing around image edges, which makes them unable to protect image edges and details. Therefore, this paper proposes an BM3D noise processing algorithm for the diffusion equation to reduce image noise without affecting image details, specifically at the edges. This method first uses anisotropic diffusion (AD) filtering for image preprocessing, and then uses the edge direction instead of horizontal direction to search for similar blocks. The AD model is mainly improved to achieve better edges and detailed processing effects. Firstly, with the improved AD direction, a 5 × 5 edge enhancement operator model is implemented in eight directions, and the corresponding gradient information is obtained. This operator improves the processed image edges to achieve clear contours and good continuity. Next, a new calculation method for the diffusion function, whose coefficient is constructed using a hyperbolic tangent function, is introduced. The proposed method is based on the link between the image gradient and diffusion function, and it is mathematically proven that the diffusion function converges faster than the diffusion function of the model proposed by Perona and Malik. Experimental results indicate that the improved model can effectively retain the image edges and texture details, avoid edge ringing, and provide significant improvements in terms of the subjective visual effects and objective numerical indicators.


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    [1] U. Erkan, D. N. H. Thanh, L. M. Hieu, S. Engínoğlu, An Iterative Mean Filter for Image Denoising, IEEE Access, 7 (2019), 167847-167859.
    [2] Z. Wang, X. Tan, Q. Yu, J. Zhu, Sparse PDE for SAR image speckle suppression, IET Image Process., 11 (2017), 425-432.
    [3] Y. Wu, G. Gao, C. Cui, Improved Wavelet Denoising by Non-Convex Sparse Regularization Under Double Wavelet Domains, IEEE Access, 7 (2019), 30659-30671.
    [4] A. Buades, B. Coll, J. M. Morel, A non-local algorithm for image denoising, 2005 IEEE Comput. Soc. Conf. Comput. Vis. Pattern Recognit., 2 (2005), 60-65.
    [5] K. Dabov, A. Foi, V. Katkovnik, K. Egiazarian, Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering, IEEE Trans. Image Process., 16 (2007), 2080-2095.
    [6] H. Zhong, K. Ma, Y. Zhou, Modified BM3D algorithm for image denoising using nonlocal centralization prior, Signal Process., 106 (2015), 342-347.
    [7] B. Shi, Q. Lian, S. Chen, X. Fan, SBM3D: Sparse Regularization Model Induced by BM3D for Weighted Diffraction Imaging, IEEE Access, 6 (2018), 46266-46280.
    [8] G. Chen, G. Luo, L. Tian, A. Chen, Noise Reduction for Images with Non-uniform Noise Using Adaptive Block Matching 3D Filtering, Chin. J. Electron., 26 (2017), 1227-1232.
    [9] Y. Li, J. Zhang, M. Wang, Improved BM3D denoising method, IET Image Process., 11 (2017), 1197-1204.
    [10] P. Perona, J. Malik, Scale-space and edge detection using anisotropic diffusion, IEEE Trans. Pattern Anal. Mach. Intell., 12 (1990), 629-639.
    [11] F. Catté, P. L. Lions, J. M. Moresl, T. Coll, Image Selective Smoothing and Edge Detection by Nonlinear Diffusion, SIAM J. Numer. Anal., 29 (1992), 845-866.
    [12] G. Gilboa, N. Sochen, Y. Y. Zeevi, Image enhancement and denoising by complex diffusion processes, IEEE Trans. Pattern Anal. Mach. Intell., 26 (2004), 1020-1036.
    [13] M. J. Black, G. Sapiro, D. H. Marimont, D. Heeger, Robust anisotropic diffusion, IEEE Trans. Image Process., 7 (1998), 421-432.
    [14] V. Bhateja, G. Singh, A. Srivastava, J. Singh, Speckle reduction in ultrasound images using an improved conductance function based on Anisotropic Diffusion, 2014 Int. Conf. Comput. Sustain. Glob. Dev., IEEE, (2014), 619-624.
    [15] C. Tsiotsios, M. Petrou, On the choice of the parameters for anisotropic diffusion in image processing, Pattern Recognit., 46 (2013), 1369-1381.
    [16] S. Tebini, Z. Mbarki, H. Seddik, E. B. Breik, Rapid and efficient image restoration technique based on new adaptive anisotropic diffusion function, Digit. Signal Process., 48 (2016), 201-215.
    [17] T. F. Chan, S. Esedoglu, F. Park, A fourth order dual method for staircase reduction in texture extraction and image restoration problems, 2010 IEEE Int. Conference Image Process., Hong Kong, (2010), 4137-4140.
    [18] G. Motta, E. Ordentlich, I. Ramirez, G. Seroussi, M. J. Weinberger, The iDUDE Framework for Grayscale Image Denoising, IEEE Trans. Image Process., 20 (2010), 1-21.
    [19] K. Liu, J. Tan, B. Su, Adaptive Anisotropic Diffusion for Image Denoising Based on Structure Tensor, 2014 5th Int. Conf. Digit. Home, IEEE, (2014), 111-116.
    [20] Y. Q. Wang, J. Guo, W. Chen, W. Zhang, Image denoising using modified Perona-Malik model based on directional Laplacian, Signal Process., 93 (2013), 2548-2558.
    [21] H. Yu, C. S. Chua, GVF-based anisotropic diffusion models, IEEE Trans. Image Process., 15 (2006), 1517-1524.
    [22] H. Tian, H. Cai, J. H. Lai, X. Xu, Effective image noise removal based on difference eigenvalue, 18th IEEE Int. Conf. Image Process., (2011), 3357-3360.
    [23] Y. Toufique, R. C. E. Moursli, L. Masmoudi, A. E. Kharrim, M. Kaci, S. Allal, Ultrasound image enhancement using an adaptive anisotropic diffusion filter, 2nd Middle East Conference Biomed. Eng., IEEE, (2014), 1-4.
    [24] H. S. Kim, J. M. Yoo, M. S. Park, T. N. Dinh, G. S. Lee, An Anisotropic Diffusion Based on Diagonal Edges, IEEE 9th Int. Conf. Adv. Commun. Technol., (2007), 384-388.
    [25] Z. Mbarki, H. Seddik, S. Tebini, E. B. Braiek, A new rapid auto-adapting diffusion function for adaptive anisotropic image de-noising and sharply conserved edges, Comput. Math. Appl., 74 (2017), 1751-1768.
    [26] J. Liu, R. Liu, Y. Wang, J. Chen, Y. Yang, D. Mag, Image denoising searching similar blocks along edge directions, Signal Process. Image Commun., 57 (2017), 33-45.
    [27] Y. Zhang, X. Han, H. Zhang, L. Zhao, Edge detection algorithm of image fusion based on improved Sobel operator, IEEE 3rd Inform. Technol. Mechatronics Eng. Conf. (ITOEC), (2017), 457-461.
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