An improved BM3D algorithm based on anisotropic diffusion equation

Yanyan Zhang; Jingjing Sun; Yanyan Zhang; Jingjing Sun

doi:10.3934/mbe.2020269

Mathematical Biosciences and Engineering

2020, Volume 17, Issue 5: 4970-4989. doi: 10.3934/mbe.2020269

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An improved BM3D algorithm based on anisotropic diffusion equation

Yanyan Zhang ^{1,2,3
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Jingjing Sun ¹

1.
Jiangsu Key Laboratory of Meteorological Observation and Information Processing, Department of Electronic and Information Engineering, Nanjing University of Information & Science Technology, Nanjing 210044, China
2.
Jiangsu Technology & Engineering Center of Meteorological Sensor Network, Nanjing 210044, China
3.
Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology, Nanjing 210044, China

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.
- anisotropic diffusion,
- diffusion function,
- edge detection,
- image gradient,
- 3D block matching algorithm
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

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Abstract

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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