中文摘要：

为了有效去除图像中的噪声，同时保留图像边缘细节，提出一种结合了偏微分方程与边缘检测的图像去噪算法。利用了You和Kaveh提出的四阶偏微分方程，该模型可以有效去除图像噪声但一个各向同性的扩散滤波器会使边缘更加模糊。为去除四阶模型引起边缘过度平滑，提出了基于边缘检测的四阶偏微分方程，新模型通过降低图像在边缘方向的扩散，得到一个有效的各向异性扩散模型，可以在去噪的同时更好地保护图像的边缘特征。实验结果表明，对比原始四阶模型该方法提高了得到的峰值信噪比与平均结构相似度。

英文摘要：

To remove the noise and preserve the edge in images, a design method of combining partial differential equation （PDE） with edge detection is presented. The fourth-order PDE introduced by You and Kaveh is effective for image noise remo- val, but it is an isotropic filter and its edge preserving ability is not satisfactory. In light of this, the edge detection is introduced into the fourth-order PDE for images restoration. Since the edge detection based fourth-order model possesses anisotropic proper- ties over the image features, it leads to improvement on noise removal and edge preserving over the original model. Experimental results indicate that the edge detection based fourth-order model improves PSNR and MSSIM compared with original model.