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。由于平面图像可以看成是二文信号，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。由于在图像的获取和转换过程中,各类图像系统中由于传感器噪声、随机大气湍流和成像光源的散射等多方面因素都要造成图像的某些降质,使图像的分辨率和对比度产生下降,造成图像的应用性大幅降低。针对这些情况，利用了小波变换良好的局部特性,使图像的信号通过小波变换后在频域上足够的分解,分离出了反映图像轮廓和细节的信息。本文结合小比分析理论，借由Matlab应用程序对数字图像进行加噪、消噪、压缩、融合、平滑、增强的数字图像处理，力求保证达到预期效果。
关键词：小波变换；小波系数；图像消噪；图像压缩；图像融合；图像增强4776
Matlab based on wavelet transform in image processing in simulation and Application
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 preprocessing．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．In the process of image gaining and switching, because of the sensor noise, the stochastic atmospheric rapids and scattering of the image formation light - source and so on, images quality, resolution and the contrast gradient will drop, and causes dramatic fall of the image application. These may create bad influence on the final recognition result. In view of this situation, this article uses the good partial characteristic of wavelet transformation, and makes the signal of image be decomposed enough in the frequency range after wavelet transformation, and separates the outline and the detail information which reflects the image. The wavelet coefficient after transforming is enhanced, then inverse transform of the wavelet coefficient is made to gain the enhanced image. The experimental result indicates that the image visual effect is improved and the image application value is enhanced.

Keywords: Wavelet transform; Coefficient of filter; Noise elimination; Image compression;  Image fusion; Image enhancement
目录

1 引言    5
1.1 课题的背景及研究意义    5
1.2 小波变换的发展    6
1.2.1小波变换的应用    6
1.1.2 小波变换国内外研究现状    7
1.3 设计工具---Matlab小波工具箱    8
2 小波函数    10
2.1二文离散小波变换函数    10
2.2二文离散小波变换的函数简介    11
3小波分析    14
3.1 连续小波变换    14
3.2连续小波变换的离散化    16
3.3 多分辨分析与Mallat算法    18
3.3.1 多分辨分析    18
3.3.2正交小波变换    20
3.3.3二文Mallat算法    21
3.4小波包变换    23
4  Matlab小波变换与图像处理    25
4.1 小波变换在图像消噪中的应用    25
4.1.1 小波图像消噪的基本原理    25
4.1.2 参数设置    26 Matlab小波变换在图像处理中的仿真及应用+源码:http://www.751com.cn/tongxin/lunwen_705.html