图像处理中扩散方程的快速数值解法

摘要

该文给出图像处理中常用的二阶非线性扩散方程的快速求解算法.首先提出一种线性差分离散格式,既包含了显格式,也包含了隐格式;其次给出了数值稳定性条件,最后讨论了3种快速解法:多重网格法(MG),交替方向隐格式(ADI),和加性算子分离格式(AOS).对3种方法进行了比较和评价,结果表明:用3种方法得到的去噪效果基本相同;ADI和AOS实现较简单;多重网格法得到的恢复图像在光滑区域视觉上优于两种直接法.%Fast algorithms for solving the 2 order nonlinear diffusion equations in image processing are presented. A linear finite difference scheme incorporating the explicit scheme and the implicit scheme is given. The stability condition of the scheme is also pgivend. Then three fast iteration algorithms including the MultiGrid (MG) method, the Alternative Direction Implicit (ADI) scheme, and the Additive Operators Splitting (AOS) schemes are discussed. Comparison of the three methods show that, the denoising performance is comparative. The MG method is a little better in denoising the smooth regions, while the ADI and the AOS schemes are simpler in realization.