基于分数阶导数的自适应各向异性扩散图像去噪模型

An Adaptive Image Denoising Model of Anisotropic Diffusion Based on Fractional Derivative

针对传统的纯各向异性扩散模型(一阶导数,用梯度表示)在平滑区域过度扩散,产生"阶梯效应"和四阶PDE(Partial Differential Equations)模型(二阶导数,用Laplace算子表示)去噪效果差的缺点,在分数阶偏微分理论的基础上提出了基于分数阶导数的自适应各向异性扩散图像去噪模型.该模型在图像的不同位置采用不同的正则化约束,具有局部自适应的特点.实验结果表明:该模型在有效去除噪声的同时,能够很好地保持图像的边缘和纹理细节信息,经过该算法处理后的图像具有更好的质量和视觉效果.

As the traditional pure anisotropic diffusion model（1order derivative used by the gradient） brings ＂staircase effect＂ by excessive diffusion in smooth regions,and the 4-order PDE（2-order derivative used by the Laplacian） model suffers poor denoising effect,an adaptive image denoising model of anisotropic diffusion based on fractional derivative was proposed.As a locally adaptive process,the proposed model adopts different regularization constraints in different parts of the image.Experimental results show that the new model not only efficiently remove noise,but also retain the edge and detail information.Better quality and visual effects of the image is achieved with this model.