基于PDE的非线性图像去噪与增强

Nonlinear Image De-Noising and Enhancement Based on PDE

应用偏微分理论,提出一种改进的基于偏微分方程的非线性图像去噪与增强方法,对传统的P-M非线性扩散模型进行改进。首先将图像变换到梯度域,然后通过改变梯度域扩散函数来达到去噪和增强的目的。与以往的时域和频域图像去噪方法相比,本文方法不仅能有效去除噪声,还能很好地保留图像的纹理细节。文章采用有限差分法将偏微分方程离散化,并结合热方程简化计算复杂度,从而实现简单快速的计算过程,为实时的图像去噪与增强处理提供保证。

Applying partial differential equation（PDE） theory,an improved algorithm of nonlinear image de-noising and enhancement was proposed based on partial differential equation by improving traditional Perona Malik nonlinear diffusion model.The image is transformed to the gradient field to achieve the purpose of image de-noising and enhancement through changing the gradient field diffusion function.Compared with the traditional spatial and frequency domain image de-noising algorithms,this algorithm can not only filter off image noise effectively,but also maintain better image texture details.This paper uses the finite difference method to discrete the partial differential equation.And it combines with the heat equation to simplify the computational complexity.So the computational process of this algorithm is simple and fast.It provides a guarantee for real-time image de-noising and enhancement processing.