Abstract: The paper researches partial differential equations that removes the noise in an image.There is a theoretical analysis on the mechanism of reduction noise.A new diffusion coefficient in partial differential equations（PDE） is built with the advantages of two existing diffusion coefficients and the proposed scheme is incorporated with the nonlinear time-dependent cooling technique for gradient threshold.The new algorithm is compared with traditional anisotropic diffusion algorithm.The results show the noises in the images are removed and the image edgedetails are reserved.The method can reduce the noise and improve the quality of the images effectively.

Key words: Gaussian noise, partial differential equations, gnisotropic diffusion algorithm, diffusion coefficient

摘要： 研究用于图像去噪的偏微分方程；在理论上对去噪原理进行了分析。通过对扩散方程中扩散系数的改进，提出了一个对噪声图像更有效、更具有适应性的去噪扩散模型，对高斯噪声图像进行处理。与传统的各向异性扩散算法进行了比较并对偏微分方程的未来发展方向进行了展望。实验结果表明，该方法在有效去除噪声的同时较好地保留了图像中的重要细节信息，使图像的细节部分清晰。该方法可以有效地去除图像噪声，提高图像的质量。

关键词: 高斯噪声, 偏微分方程, 各项异性扩散算法, 扩散系数