Abstract: PDE’s（Partial Differential Equations） is extended to smooth multi-valued images in an anisotropic manner in this paper．Starting from a review of existing anisotropic schemes on diffusion PDE’s，point out the pros and cons of the different equations include the divergence-based PDE and the trace-based PDE．After re-build the eigenvalues and the diffusion tensors，a new tensor-driven diffusion PDE equation witch is proposed，that coupling between anisotropic diffusion and shock filters．Results show that the new model can not only well restrain noise but also enhance edge and keep much more details of images．

Key words: anisotropic smoothing, shock filter, diffusion tensor, eigenvalue, eigenvector, color image filtering

摘要： 将扩散偏微分方程PDE’s推广到彩色图像滤波。分析了基于散度算子和基于迹算子PDE的优缺点，提出了一个新的扩散PDE方法。该方法在各向异性扩散基础上增加了一个震动滤波算子，并对特征根和扩散张量进行了重构，不仅对图像有很好的滤波效果，而且对边缘有增强保护的作用。实验结果表明，提出的方法达到了既有效去除噪声又保留更多细节的目的。

关键词: 各向异性扩散, 震动滤波, 扩散张量, 特征向量, 特征根, 彩色图像滤波