一种小波阈值函数构建的图像去噪算法研究

Image Denoising Algorithm Based on Wavelet Threshold Function

针对一些混合噪声在图像处理过程中存在的问题及经典的图像去噪算法进行分析,以小变换为基础,提出一种小波阈值函数构建的图像去噪算法。研究过程以加性高斯和乘性斑点两种图像噪声的模型构建为基础,找出图像噪声出现概率的分布函数是区分和有效控制噪声的前提条件;通过对小波阈值去噪的原理进行分析,明确小波阈值去噪的小波频率分解、构建小波阈值函数及计算函数、重构图像三个关键流程;通过对硬阈值、软阈值和半软半硬阈值三种图像去噪算法进行分析,找出三种算法中存在的关键问题,提出在阈值处具有连续性、阈值函数具有线性、阈值函数具有可微可导性、计算的阈值结果在预估阈值区域具有平滑过度性,是获取最佳阈值计算结果的四个重要条件。针对阈值函数的构建,采用MATLAB仿真实验,对硬阈值算法、软阈值算法和本文阈值算法进行线性处理后的输出结果统计;以三幅实验图像为对象,对硬阈值算法、半软半硬阈值算法和本文提出的算法进行去噪效果统计;并根据图像去噪的主要目的所在,对采用的三种算法进行图像去噪后,进行图像边缘特征提取实验。实现结果表明:本文算法中构建的阈值函数,在理想阈值和预估阈值相等处都具有连续性,所确定的小波平缓系数,起到较好的平滑作用,且有助于求导计算。

In this paper,the problems of some mixed noise in image processing and the classical image denoising algorithm are analyzed.Based on the small transform,an image denoising algorithm based on wavelet threshold function is proposed.The research process is based on the model construction of additive Gaussian and multiplicative speckle.The distribution function of image noise occurrence probability is found out,which is the precondition of distinguishing and controlling noise effectively.By analyzing the principle of wavelet threshold de⁃noising,three aspects of wavelet threshold de-noising,including wavelet frequency decomposition,constructing wavelet threshold func⁃tion and calculation function,and image reconstruction,are clarified Through the analysis of three image denoising algorithms:hard threshold,soft threshold and semi soft semi hard thresholding,the key problems in the three algorithms are found out.It is proposed that the threshold has continuity,the threshold function has linearity,the threshold function has differentiability,and the calculated threshold result has smooth transition in the estimated threshold area,which is the best threshold calculation result Four important conditions of fruit.For the construction of threshold function,matlab simulation experiment is used to make statistics of the output results of the hard threshold algorithm,soft threshold algorithm and the threshold algorithm in this paper after linear processing;taking three experimental images as the object,the denoising effect of the hard threshold algorithm,the semi soft semi hard threshold algorithm and the algorithm proposed in this paper are statistically analyzed;and according to the main purpose of image denoising,the denoising effect of the pro⁃posed algorithm is analyzed After image denoising by three algorithms,the experiment of image edge feature extraction is carried out.The results show that:the threshold function constructed in this algorithm has continuity at the place where the ideal threshold and the predict⁃ed threshold are equal,and the determined wavelet smoothing coefficient plays a good smoothing role and is helpful to the derivation cal⁃culation.