进一步研究了基于偏微分方程的图像去噪方法。为了去除二阶偏微分方程(P-M 模型)引起的阶梯效应以及提高四阶偏微分方程(Y-K 模型)的边缘及纹理保护能力，本文将梯度矢量卷积场(GVC)引入到四阶偏微分方程Y-K模型中，提出了基于GVC的四阶各向异性扩散模型。首先，减去原始Y-K模型中的部分梯度方向扩散。然后，引入GVC场以代替图像在梯度方向的二阶导数直接计算。由于GVC场可以较准确地确定图像的边缘位置，并对噪声具有很强的鲁棒性，因此得到了有效的各向异性扩散模型。实验结果表明，运用本文去噪方法可以更好地保护图像边缘及纹理等细节特征，而且能够有效地提高峰值信噪比; 文中所有在实验中得到的峰值信噪比均比原始模型高1 dB以上。

The image denoising methods based on Partial Differential Equations (PDEs) were explored. In order to alleviate the staircase effect in second-order PDE (P-M model) and improve the ability of edge and texture preserving of fourth-order PDE (Y-K model), the Gradient Vector Convolution (GVC) field was introduce into the fourth-order PDE, and a four-order anisotropism diffusion model was established. Firstly, the parts of diffusion in the direction of gradient was subtracted. Then, the GVC field was introduced to replace the calculation of second derivative. Because of the robustness of GVC and its outstanding ability of detecting edge, an effective anisotropic diffusion model was obtained. Experimental results indicate that the GVC based fourth-order model can protect the details over the original model like edge and texture features better and can improve the Peak Signal to Noise Ratio(PSNR).The PSNRs in experiments have been improved more than 1 dB as compared with that original Y-K model.