小波阈值去噪及MATLAB仿真

-I- 摘 要

小波分析理论是一种新兴的信号处理理论，它在时间上和频率上都有很好的局部性，这使得小波分析非常适合于时—频分析，借助时—频局部分析特性，小波分析理论已经成为信号去噪中的一种重要的工具。利用小波方法去噪，是小波分析应用于实际的重要方面。小波去噪的关键是如何选择阈值和如何利用阈值来处理小波系数，通过对小波阈值化去噪的原理介绍,运用MATLAB 中的小波工具箱，对一个含噪信号进行阈值去噪，实例验证理论的实际效果，证实了理论的可靠性。本文设计了几种小波去噪方法，其中的阈值去噪的方法是一种实现简单、效果较好的小波去噪方法。

关键词：小波变换；去噪；阈值

-II- Abstract

Wavelet analysis theory is a new theory of signal process and it has good

localization in both frequency and time do-mains.It makes the wavelet analysis

suitable for time-frequency analysis.Wavelet analysis has played a particularly

impor-tant role in denoising,due to the fact that it has the property of time- frequency

analysis. Using wavelet methods in de-noising, is an important aspect in the

application of wavelet analysis. The key of wavelet de-noising is how to choose a

threshold and how to use thresholds to deal with wavelet coefficients. It confirms the

reliability of the theory through the wavelet threshold de-noising principle, the use of

the wavelet toolbox in MATLAB, carrying on threshold de-noising for a signal with

noise and actual results of the example confirmation theory.In this paper,the method

of Wavelet Analysis is analyzed.and the method of threshold denoising is a good

method of easy realization and effective to reduce the noise.

Keywords：Wavelet analysis；denoising；threshold

-III- 目 录

摘 要 ........................................................................................................................... I

Abstract ........................................................................................................................ II

第1章 绪论 ................................................................................................................ 1

1.1 研究背景和意义 ............................................................................................ 1

1.2 国内外研究历史和现状 ................................................................................ 2

1.3 本文研究内容 ................................................................................................ 4

第2章 小波变换的基本理论 .................................................................................... 5

2.1 傅立叶变换 .................................................................................................... 5

2.2 加窗傅立叶变换 ............................................................................................ 6

2.3 小波变换 ........................................................................................................ 7

2.3.1 连续小波变换 ...................................................................................... 8

2.3.2 离散小波变换 ...................................................................................... 9

2.4 多分辨分析 .................................................................................................. 12

本章小结 ............................................................................................................. 13

第3章 经典噪声类型及去噪方法 .......................................................................... 14

3.1 经典噪声类型 .............................................................................................. 14

3.2 常用滤波器 .................................................................................................. 17

3.2.1 线性滤波器 ........................................................................................ 18

3.2.2 均值滤波器 ........................................................................................ 18

3.2.3 顺序统计滤波器 ................................................................................ 19

3.2.4 其他滤波器 ........................................................................................ 19

3.3 经典去噪方法 .............................................................................................. 20

3.4 Matlab工具 .................................................................................................. 21

3.4.1 Matlab 发展历程 ............................................................................... 21

3.4.2 Matlab 简介 ....................................................................................... 21

本章小结 ............................................................................................................. 22

第四章 小波阈值去噪及MATLAB仿真 ............................................................. 23

4.1 小波阈值去噪概述 ...................................................................................... 23

4.1.1 小波阈值去噪方法 ............................................................................ 24

4.1.2 图像质量评价标准 ............................................................................ 24

4.2 基于MATLAB的小波去噪函数简介 ....................................................... 25