基于全变分模型的图像噪声去除效果比较

Comparison of image denoising based on total variation model

基于偏微分方程的图像去噪方法由于将数学与工程结合得更加紧密,具有较强的自适应能力和灵活性。本文首先介绍了目前已经提出的变分模型的快速Split-Bregman算法,然后通过大量数值实验对不同模型的去噪效果进行了比较。所研究的模型包括L1范数、L2范数、LTV(1ayered total variation)规则项、MTV(multicharmel total variation)规则项和CTV(color total variation)规则项,从灰度图像和彩色多通道图像两方面进行分析。实验结果表明对于灰度图像基于L1范数的TV去噪模型效果较好,彩色图像中CTV模型对图像去噪边缘保持最好,其他依次是MTV模型、LTV模型。

The image denoising method that based on partial differential equation combines mathematics and engineering has strong adaptability and flexibility of the PDE. In this paper, we first design a fast Split-Bregman algorithm for this kind of variational models, and then we compare the denoising results of different models by a large number of numerical experiments. Mainly from the two aspects of grayscale images and color images by L1 norm, L2 norm and regularization of LTV, MTV, CTV. The experimental results show that the TV denoising model based on L1 norm has a better effect on the gray image, and the CTV model in the color image has the best effect on the edge of image denoising, and the other is MTV model, LTV model.