基于偏微分方程的图像修复方法研究

针对全变分（TV）模型在各参考点具有相同权值的情况，以待修复区域像素点的梯度值为信息构造出一个扩散函数，利用此扩散函数控制各参考点的权值；结合非线性扩散思想，提出一个针对时间参数的自适应迭代函数。扩散函数与自适应迭代函数共同作用，进行图像修复。实验结果表明，本文提出的新方法修复效果好且用时少。

Image restoration method based on partial differential equations

For the case in which the original model has the same weight at each reference point on a TV model, the paper propose a new concept whereby a diffusion function based on the gradient value of the pixels in the area to be repaired is constructed. The diffusion function is used to control the value of the contribution of each reference point. In addition, an adaptive iterative function for time parameters based on the idea of nonlinear diffusion is proposed. The diffusion function and adaptive iterative function work together to complete the image inpainting. Results of the experiment reveal that the new method proposed in this paper can achieve good processing effect in less time.