应用对偶方法的TV图像去噪

Total variation-based image noise removal using dual method

介绍了基于梯度算子和基于拉普拉斯算子的TV模型图像去噪,指出了传统模型求解过程中存在不可微项的问题,对传统模型进行改进,提出了基于梯度算子和拉普拉斯算子相结合的TV模型,并用对偶方法求其数值解。引入对偶变量,解决了传统的最优化方法求解过程中存在不可微项的问题,使得所求得的数值解更加接近于原始图像。最后通过实验验证,证明该方法能有效去除噪声,同时能够保持图像边缘,减弱传统模型产生的阶梯效应,并能大幅提高去噪效率。

TV image de-noising model is introduced either based on gradient operator or based on Laplacian operator.The non-differentiability problem of the traditional method is studied.To improve the traditional method,the TV model based on the combination of gradient operator and Laplacian operator is put forward with a dual method to get the numerical solution.The new method eliminates the non-differentiability problems of the traditional method through a dual variable,and yields the numerical solution more precise to the one of the original image.Experiments show that the new method can remove noise effectively,keep the image edge,attenuate the staircase effect of the traditional method,and improve de-noising efficiency a lot.