基于变分偏微分方程的双参数图像去噪模型

摘要

给出了一种基于变分偏微分方程的双参数图像去噪模型.利用变分法的极大极小原理,证明了该双参数模型存在唯一的极小值,给出该模型的Euler-Lagrange方程,根据给出的偏微分方程的离散格式,对噪声图像进行去噪,与Rudin,Osher and Fatemi提出的模型(ROF模型)的结果比较,结果表明,双参数模型在视觉上及峰度信噪比上都比ROF模型的去噪效果好.%This paper presents an image denoising model based on Variational Partial differential equation with double parameters. Firstly,using the minimax principle of variational method,this paper proves that the double parameters model has an unique minimal value,then it gives the corresponding Euler-Lagrange equation. Secondly,According to the given discrete format of partial differential equation,it denoises some noise images. Comparing the results with Rudin,Osher and Fatemi model(ROF model) ,the results show that double parameters model in visual and kurtosis signal-to-noise ratio has better denoising effect.