一种改进的基于小波偏微分方程的图像去噪方法

An improved algorithm for image noise removal based on wavelet transform and partial differential equations

提出一种基于小波分解和四阶偏微分方程相结合的方法用于图像去噪,利用小波良好的时频局域化特性和偏微分方程能够很好地保留图像的边缘和细节的特点对图像噪声进行消除.传统的二阶线性扩散方程计算效率低,易产生阶梯效应,这里采用一种用拉氏锐化算子替代拉普拉斯算子的四阶偏微分方程模型.实验结果表明,本方法是一种高效的去除噪声并能很好地保持图像边缘的算法.

This paper presents a method for image noise removal based on wavelet transform and 4th order partial differential equations （PDE）. Wavelet transform has better time-frequency localization properties and partial differential equation can retain image＇ s edge and details, so the proposed method can remove noise by taking advantage of these characteristics. The traditional 2nd order linear diffusion equation has low computation efficiency and is apt to get into ladder effect. Therefore the authors propose a new 4th order PDE model, which adopts Laplacian -sharpening operator instead of Laplacian operator. The experimental results show that this method is an efficient algorithm which does well in removal of noise and keeping image＇ s edge.