基于空间分数阶偏微分方程的图像去噪模型研究

为了在获取更高信噪比的同时更多地保留图像边缘和纹理等细节信息，将分数阶微积分理论和偏微分方程方法有效结合，构建了基于空间分数阶偏微分方程的图像去噪模型，并利用分数阶微分掩模算子来实现去噪模型的数值计算。该去噪模型通过引入以分数阶梯度模值为参数的边缘停止函数并选择合适的分数阶微分阶次，由此能够在一定程度上解决传统去噪模型存在的不足之处。实验结果表明，基于空间分数阶偏微分方程的图像去噪模型较传统的去噪模型不仅可以提高图像的信噪比，而且可以更好地保留图像边缘和纹理等细节信息。

Research on Image Denoising Based on Space Fractional Partial Differential Equations

In order to preserve more edge and texture information of image while obtaining higher value of signal-to-noise, the image denoising model based on space fractional partial differential equations was constructed by effective combination of theory of fractional calculus and methods partial differential equations, and the numerical of denoising model was achieved using fractional differential mask operator. The denoising model proposed in this paper could solve existing problems of the traditional denoising model to a certain extent by introducing the edge stopping function to the parameters of fractional grads modulus and selecting the appropriate order of fractional differential. The experimental results show that the image denoising model based on space fractional partial differential equations proposed in this paper compared with the traditional image denoising models not only enhanced the signal-to-noise ratio of image but also better retained the edge and texture details information of image.