应用原对偶方法光滑向量的四阶算子分裂方法

高阶算子分裂方法在改善图像边缘阶梯化、提高计算效率等问题上有很好的作用,其主要思想是将四阶的偏微分方程分裂成两个二阶的偏微分方程分别求解,先进行向量光滑,然后再进行图像重构。相对于第一步的一般显式数值迭代方法,本文应用原对偶格式进行变量替换,应用拟牛顿进行向量光滑。数值结果表明,该方法很好地提高了信噪比,且视觉效果显著。

An Efficient Primal-Dual Technique Applied in the Operator-Splitting Method for Noise Removal in Images

The operator-splitting method of the fourth-order partial differential equations is efficient both in modifying the disadvantage of stair-case effect and in increasing computational efficiency.The removal is done by two steps,first using a TV filter to smooth the normal vectors of the level curves of the noise,and then trying to find a surface to fit the smoothed normal vectors.In this paper,a primal-dual method is applied in the first step instead of finite difference schemes.We use the Newton method to sm...