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An improved BM3D algorithm based on anisotropic diffusion equation
Mathematical Biosciences and Engineering Pub Date : 2020-07-17 , DOI: 10.3934/mbe.2020269
Yanyan Zhang , , Jingjing Sun , ,

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.

中文翻译:

一种基于各向异性扩散方程的改进BM3D算法

传统的3D块匹配(BM3D)算法是目前最好的降噪方法之一。但是,它们表现出在图像边缘周围响起的问题,这使它们无法保护图像边缘和细节。因此,本文针对扩散方程提出了BM3D噪声处理算法,以减少图像噪声而不影响图像细节,特别是在边缘。该方法首先使用各向异性扩散(AD)滤波进行图像预处理,然后使用边缘方向而不是水平方向搜索相似的块。AD模型主要进行了改进,以实现更好的边缘和详细的处理效果。首先,利用改进的AD方向,在八个方向上实现5×5边缘增强算子模型,并获得相应的梯度信息。该操作员改善了处理后的图像边缘,以获得清晰的轮廓和良好的连续性。接下来,介绍了一种新的扩散函数计算方法,该函数的系数是使用双曲正切函数构造的。所提出的方法是基于图像梯度和扩散函数之间的联系,并且数学证明了扩散函数的收敛速度比Perona和Malik提出的模型的扩散函数快。实验结果表明,改进后的模型可以有效地保留图像边缘和纹理细节,避免边缘振铃,并在主观视觉效果和客观数值指标方面提供了显着改善。介绍了使用双曲正切函数构造其系数的方法。所提出的方法是基于图像梯度和扩散函数之间的联系,并且数学证明了扩散函数的收敛速度比Perona和Malik提出的模型的扩散函数快。实验结果表明,改进后的模型可以有效地保留图像边缘和纹理细节,避免边缘振铃,并在主观视觉效果和客观数值指标方面提供了显着改善。介绍了使用双曲正切函数构造其系数的方法。所提出的方法基于图像梯度和扩散函数之间的联系,并且数学证明了扩散函数的收敛速度比Perona和Malik提出的模型的扩散函数快。实验结果表明,改进后的模型可以有效地保留图像边缘和纹理细节,避免边缘振铃,并在主观视觉效果和客观数值指标方面提供了显着改善。数学上证明了扩散函数的收敛速度比Perona和Malik提出的模型的扩散函数快。实验结果表明,改进后的模型可以有效地保留图像边缘和纹理细节,避免边缘振铃,并在主观视觉效果和客观数值指标方面提供了显着改善。数学上证明了扩散函数的收敛速度比Perona和Malik提出的模型的扩散函数快。实验结果表明,改进后的模型可以有效地保留图像边缘和纹理细节,避免边缘振铃,并在主观视觉效果和客观数值指标方面提供了显着改善。
更新日期:2020-07-20
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