1、 太原理工大学现代科技学院毕业设计（论文） I 傅里叶变换与小波变换在图像去噪中的应用 摘要 图像去噪是图像处理研究的一个重要话题。图像在获取和传输的过程中经常要受到噪声的污染。噪声对图像质量有着非常重要的影响。所以 ,必不可免的图像去噪成为图像分析和处理的重要技术。 用传统傅里叶变换对信号去噪的基本思想是对含噪信号进行傅里叶变换后使用低通或带通滤波器滤除噪声频率 ， 然后用逆傅里叶变换恢复信号。但是傅里叶变换很难将有用信号的高频部分和由噪声引起的高频干扰有效地区分开。 小波分析是傅里叶分析思想方法的发展和延拓，与傅里叶分析密切相关。而小波阈值去噪方法是众 多图象去噪方法中的佼佼者 ,它利用图
2、象的小波分解后 ,各个子带图象的不同特性 ,选取不同的阈值 ,从而达到较好的去噪效果。而且与传统的去噪方法相比较 ,有着无可比拟的优点 ,成为信号分析的一个强有力的工具 ,被誉为分析信号的显微镜。 本文概述了傅里叶变化与小波变换去噪的基本原理及其比较。对常用的几种去噪方法进行了分析。最后结合理论分析和实验结果。在实际的图像处理中，实现了小波变换去噪法的处理。 关键词 ： 小波变换 ，图像去噪， Matlab 太原理工大学现代科技学院毕业设计（论文） II Application of image de-noising based on Fourier transform and wavelet
3、 transform ABSTRACT Image de-noising is an eternal theme of the image processing research. Image acquisition and transmission process often subject to noise pollution. The noise has a very important impact on image analysis. So, the image de-noising become an important technology for image analysis
4、and processing. The basic idea in the signal de-noising using the traditional Fourier transform is a Fourier transform of the noisy signal using a low-pass or band-pass filter to remove the noise frequency and then inverse Fourier transform signal. But Fourier transform is difficult to be useful to
5、the high frequency part of signal and high frequency noise caused by interference efficiently. Wavelet analysis is a Fourier analysis of the development and continuation of the way of thinking, has been closely related to the Fourier analysis. Wavelet threshold method is the leader in the number of
6、image de-noising method, its use of the wavelet decomposition, the different characteristics of each sub-band image, select a different threshold, so as to achieve better de-noising effect . Following the Fourier transform after momentary frequency analysis tool, has the characteristics of the local
7、 nature and multi-resolution analysis in the frequency domain at the same time, not only to meet a variety of de-noising requirements, such as low-pass, Qualcomm, random noise removal, and compared with the traditional de-noising method has unparalleled advantages to become a powerful tool in signal
8、 analysis, known as the analytical signal mathematical microscope. This article provides an overview of the basic principles of the Fourier transform and wavelet transform de-noising. Several commonly used de-noising method are analyzed . Finally, the theoretical analysis and experimental results, discussed the factors that affect the de-noising performance in a complete de-noising algorithm. In practical image processing, the processing of the wavelet transform de-noising method. KEY WORDS: wavelet transform, image de-noising, Matlab
