摘要一直以来图像在我们的生活中扮演着重要的角色，但是，我们对于图像质量的要求也越来越高。因此，用小波分析用于图像去噪的研究应用也越来越广泛。

由于图像在产生传播的过程中会受到影响，原始图像会变成含噪图像，而噪声会影响图像的质量，因此去除图像中的噪声是至关重要的。84093

本文是以图像去噪为主要内容,分别介绍了小波分析的基本理论,多分辨率分析和Mallat算法,以及传统去噪方法去噪原理和算法。同时对传统图像去噪和小波分析去噪的性能进行分析比较。并且重点介绍和分析了小波阈值去噪。经过实验的仿真分析表明：小波阈值去噪的PSNR会比经典传统去噪方法的PSNR低一些。这一结论表明小波去噪方法的性能是优于传统去噪方法的。而小波去噪的实验仿真结果表明当噪声的方差增大时，图像的PSNR会随之减小。软阈值函数去噪的性能也是优于硬阈值函数的。并且小波包分析去噪法的性能优于小波去噪法

关键词:小波分析；Matlab；图像去噪；噪声

Abstract Image has been playing an important role in our life,but, our requirements for image quality are also getting higher and higher。Therefore, the application of wavelet analysis in image denoising is more and more widely used。

As the image in the process of producing the transmission is affected, the original image will become a noisy image, and the noise will affect the quality of the image, it is essential to remove the noise in the image。

This paper mainly introduces the basic theory of wavelet analysis, which is the main content of image denoising, Multi-Resolution Analysis and Mallat Algorithm, as well as the traditional denoising method to the denoising principle and algorithm,as well as the traditional denoising method based on the denoising principle and algorithm。At the same time, the performance of denoising and wavelet analysis of traditional image denoising are analyzed and compared。 And focus on the introduction and analysis of the wavelet threshold denoising。 The simulation analysis shows：Wavelet threshold denoising PSNR will be lower than the classical denoising method of PSNR。 This conclusion shows that the performance of the wavelet denoising method is better than that of the traditional denoising method。However, experimental simulation results Wavelet denoising show that when the variance of the noise increases, the PSNR of the image will be reduced。 Soft threshold function denoising performance is also better than the hard threshold function。and Wavelet packet analysis denoising method is better than the wavelet denoising method。

Keywords:  wavelet  analysis ;  Matlab ; image noise reduction ; noise 

目录

第一章 绪论 1

1。1  研究背景 1

1。2  小波分析的发展史 2

1。3  小波分析的研究状况 3

1。4  小结 5

第二章  图像去噪方法的研究 6

2。1  图像中的噪声及分类 6

2。2  图像质量的评价标准 6

2。3  传统图像去噪方法的研究 8

2。4  本章小结 9

第三章 小波分析的理论基础 10

3。1  小波分析基础 10

3。1。1  一维傅里叶变换 10

3。1。2  二维傅里叶变换