中文摘要：

本文提出了一个新的边缘定向增强扩散模型．针对现有各向异性扩散方程中，边缘增强扩散模型不能正确地对边缘定向，而相干增强扩散模型易在光滑处产生虚假边缘的缺点，本文的模型采用基于非线性光滑算子的边缘定向算子对边缘定向，并根据边缘的位置和方向设置扩散张量的特征根，使其在光滑区域沿边缘方向和垂直边缘方向均具有较大值，而在边缘区域垂直边缘方向值小，沿边缘方向值大，从而达到既保护边缘又去除噪声的目的，在整幅图像上均具有较好的去噪效果．理论分析和数值计算结果均表明，本文方法具有比现有扩散去噪方法更好的去噪效果，同时在峰值信噪比和边缘保护指数方面具有显著优势．

英文摘要：

This paper puts forward a new edge-directed enhancing based anisotropic diffusion model. Since edge enhancing diffusion can not get right edge direction, and coherence enhancing diffusion often induces false edges in image denoising, our new model adapts a new operator for edge orientation based on nonlinear smoothing operator, and defines eigenvalues on edge＇s orientation such that the new tensor has large eigenvalues in both gradient direction and edge direction on the slippy region of image, but has small eigenvalues in gradient direction and large eigenvalues in edge direction on the edge region of image. So it can remove noise efficiently and keep edges better at the same time to get good result on the whole image. Both theory analysis and numerical results show that the new model has better denosing results than the known diffusion model, and has higher peak signal to noise ratio and higher edge preserved index.