修正的TV-Stokes模型的新快速算法

基于Tai等人的前期工作,本文研究修正的TV-Stokes图像去噪模型,提出一些新的求解该两步模型的快速算法.我们利用对偶形式和多重网格方法得到一个求解第1步的快速算法.给出另外一种新的求解光滑的切向量场的保不可压性质的算法.在第2步中,我们提出一类有效的全新算法:首先通过计算Poisson方程得到具有光滑法向量场的函数g,然后利用Jia和Zhao的方法得到恢复的图像.新算法的运算速度非常快,用于图像恢复的CPU时间少于0.1 s.数值结果显示新的快速算法是有效的和稳定的,恢复图像的质量也超过了一般去噪方法.

New fast algorithms for a modified TV-Stokes model

Based on some previous work of Tai et al., the modified TV-Stokes models for image denoising are considered. In this paper, we present some new fast algorithms for the modified TV-Stokes models. In the first step, we use the dual formulation of denoising and multigrid method to get a fast algorithm. Another new imcompressibility-preserved algorithm is proposed for the tangent field smoothing. In the second step, completely new algorithms are presented by us. A function g fitting the smoothing normal field is computed by the Poisson equation. Then, restored image is obtained efficiently by using the algorithm of Jia and Zhao. This new method is very fast such that the CPU time in the reconstruction step is less than 0.1 s. Numerical results demonstrate that our new algorithms are efficient and robust. The restored images are better than the general denoising methods.