基于MATLAB的小波变换在信号分析中应用的实现

基于MATLAB的小波变换在信号分析中应用的实现

院系：应用技术学院

专业：电子信息工程

*名：***

指导教师单位：应用技术学院

指导教师姓名：王庆平

指导教师职称：讲师

二零一一年六月

The application of wavelet transform based on MTLAB in signal

analysis

Faculty：Application and Technology Institute

Profession：Electronic information engeering

Name：Li Chengyun

Tutor’s Unit：Application and Technology Institute

Tutor：Wang Qingping

Tutor’s Title：Lecturer

June 2011

目录

摘要 (1)

ABSTRACT (2)

前言 (3)

第1章绪论 (4)

1.1本文的研究背景意义 (4)

1.2国内外研究现状 (5)

1.3本文的研究内容 (7)

第2章 MATLAB简介 (8)

2.1MATLAB的概况 (8)

2.2MATLAB6.1的功能 (8)

2.3MATLAB的主要组成部分 (9)

2.4MATLAB的语言特点 (10)

第3章基本理论 (12)

3.1从傅里叶变换到小波变换 (12)

3.1.1 傅里叶变换 (12)

3.1.2 短时傅里叶变换 (13)

3.1.3 小波变换 (14)

3.2连续小波变换 (15)

3.3离散小波变换 (17)

3.4小波包分析 (18)

3.5多分辨率分析与M ALLAT算法 (19)

3.5.1 多分辨率分析 (19)

3.5.2 Mallat算法 (19)

3.6本章小结 (20)

第4章小波阈值法图像去噪 (21)

4.1图像去噪 (21)

4.1.1 邻域平均法 (22)

4.1.2 中值滤波法 (24)

4.2小波阈值去噪 (27)

4.2.1 阈值去噪原理 (28)

4.2.2 选取阈值函数 (28)

4.2.3 几种阈值选取方法 (29)

4.3小波阈值仿真 (31)

第5章小波变换在图像边缘检测中的应用 (33)

5.1图像边缘检测概述 (33)

5.2常见的边缘检测算法。 (34)

5.3小波边缘检测算法 (39)

5.4小波缘检测仿真 (39)

全文总结 (42)

谢辞 (43)

参考文献 (44)

附录 (46)

英文资料 (46)

中文翻译 (60)

摘要

小波分析理论作为新的时频分析工具，在信号分析和处理中得到了很好的应用。平面图像可以看成是二维信号，因此，小波分析很自然地应用到了图像处理领域。图像去噪和边缘检测是图像预处理中应用非常广泛的技术，其作用是为了提高信噪比，突出图像的期望特征，以便对其进行更高层次的处理。小波变换由于其自身的优良特性而在图像处理中得到了越来越多的应用。

本文从基本理论出发，首先对小波变换进行了详尽而深刻的阐述。循序渐进地介绍了从概念到小波分析等一系列相关内容，最终引出小波分析中非常重要的Mallat 算法。对小波变换在图像去噪和边缘检测领域的应用本文作了重点研究。为用作对比，简要介绍了几种传统的图像去噪算法和边缘检测算法，重点研究和详细阐述了运用小波变换进行图像去噪和边缘检测算法的原理和具体实现步骤,将小波算法与传统的图像去噪算法和边缘检测算法作MATLAB仿真对比以得出结论。

关键词：图像去噪；图像边缘检测；小波变换；MATLAB

ABSTRACT

Wavelet analysis theory, as a new time—frequency analysis tool，has been well applied in the area of signal analysis and processing．An image is actually a two-dimensional signal．So it is natural to apply wavelet analysis to the area of image processing．Image de-noising and edge detection are two widely used technologies in image pre—processing．By enhancing SNR and highlighting expected features of image，it will be more convenient for further step of processing．Wavelet transform is more and more frequently applied to image processing according to its own advantages．First，beginning with basic theories，wavelet transform is thoroughly and deeply introduced in this article．A series of related contents from definition to wavelet analysis are gradually elaborated step by step．Mallat algorithm which is of great importance in wavelet analysis is introduced in the end．

Second，researches on application of wavelet transform to the areas of image de—noising and edge detection are the major part of this article．For comparison，several traditional image de—noising methods and edge detection methods are briefly introduced．The theories and steps of completion of image de—noising and edge detection algorithms to which wavelet transform is applied are elaborated．Image de—noising and edge detection algorithms between wavelet transform and traditional methods are simulated and compared to draw a conclusion．

Key words：image de-noising；image edge detection；wavelet transform; MATLAB