Abstract: An improved method for image restoration is presented in this paper，which is based on least-squares and regularization method.Firstly fourth-order partial differential equations are used to remove the blurred image’s noise to get a transition image，and then the least-squares and regularization methods are adopted to deal with the transition image to get a final image.The experimental results show that the method not only overcomes ill-posed problem，but also the restored image’s visual effect and peak signal to noise ratio are improved significantly compared with least-squares and regularization methods.

Key words: image restoration, least-squares, regularization, fourth-order partial differential equations

摘要： 在常用的最小二乘正则化方法的基础上，提出了一种改进的图像复原方法。在运算中，首先用四阶偏微分方程方法对模糊图像进行噪声处理，得到一幅中间图像，然后对这个中间图像采用最小二乘正则化方法进行处理，便得到了最终的复原图像。实验表明，该方法不仅能克服问题的病态性，而且复原后的图像比最小二乘正则化方法复原后的图像整体视觉效果和峰值信噪比都有明显的提高。

关键词: 图像复原, 最小二乘, 正则化, 四阶偏微分方程