中文摘要：

为克服四阶各向同性扩散方程模糊图像边缘和四阶各向异性扩散方程引起阶梯伪影的不足，提出基于自适应四阶偏微分方程的图像去噪算法。采用图像梯度模构建关于图像特征信息的检测函数；针对图像不同的特征，采用特征检测函数自适应地调整图像在法线和切线方向扩散系数的指数。在平坦和斜坡区域采用各向同性扩散去除噪声，在图像边缘点处采用各向异性扩散保护图像特征。实验结果表明，该算法结合了四阶各向同性扩散和异性扩散方程的优势，在去噪和保边之间实现了很好的平衡。

英文摘要：

To overcome the deficiencies that the fourth-order isotropic diffusion equation blurs image edges and the fourth-order anisotropic diffusion equation causes staircase artifacts,an image denoising algorithm based on the adaptive fourth-order partial differential equation was proposed.The modulus of the image gradient was introduced to construct the detection function of the image feature information.According to different features of the image,the exponents of diffusion coefficients in normal and tan-gent directions were adaptively adjusted using the feature detection function.Isotropic diffusion was adopted to remove noise in flat and ramp regions and anisotropic diffusion was used to preserve image characteristics of edge points.The experimental re-sults show that the algorithm combines the advantages of the fourth-order isotropic diffusion equation and fourth-order anisotro-pic diffusion equation,achieving a good tradeoff between noise removal and edge preservation.