【作者】 韦力强；

【导师】 谭阳红；

【作者基本信息】 湖南大学 ， 电工理论与新技术， 2007， 硕士

【摘要】 小波变换是一种新型的数学分析工具,是80年代后期迅速发展起来的新兴学科。小波变换具有多分辨率的特点,在时域和频域都具有表征信号局部特征能力,适合分析非平稳信号,可以由粗及精地逐步观察信号。小波分析的理论和方法在信号处理、图像处理、语音处理、模式识别、量子物理等领域得到越来越广泛的应用,它被认为是近年来在工具及方法上的重大突破。信号的采集与传输过程中,不可避免会受到大量噪声信号的干扰,对信号进行去噪,提取出原始信号是一个重要的课题。Donoho的硬阈值和软阈值去噪方法在实际中得到广泛的应用,而且也取得了较好的效果。但是硬阈值函数的不连续性导致重构信号容易出现Pseudo-Gibbs(伪吉布斯)现象;而软阈值函数虽然整体连续性好,但估计值与实际值之间总存在恒定的偏差,具有一定的局限性。此后的众多文献都是在Donoho的去噪方法基础上作了一定的改进。这些方法一定程度提高了信号的信噪比,达到了去噪的目的。为了得到最好的去噪效果,不但要选择合适的小波函数,还要确定最佳的分解层数并选取合适的阈值。阈值的选取直接影响到最终的去噪效果,如何最大限度去除噪声的同时保留信号的原始特征是去噪过程中的一个难点,如果阈值选取过小,则会出现消噪不足,过多的保留了噪声,致使信号的弱特征成分被噪声淹没;如果阈值选取过大,则会出现过消噪,将信号中的弱特征误认为噪声消除。当信号所含噪声的水平不同,去噪时采用的阈值也应有所不同。本文从小波变换的定义和信号与噪声的不同特性出发,在对比分析了各种去噪方法的优缺点基础上,本文先构造了一个新的阈值函数,同Donoho的阈值函数相比,新阈值函数具有表达式简单,连续性好且高阶可导的优点,便于进行各种数学处理。本文提出了一维信号去噪的新方法,该方法对去除一维平稳信号含有的白噪声有非常满意的效果,具有有效性和通用性,能提高信号的信噪比。将该方法应用于语音信号去噪,对单个的字词语音的去噪效果比较满意,能有效去除语音信号含有的白噪声,提高了语音的信噪比和可识别性。通过对二维图像信号的研究,本文提出了基于小波变换的二维信号去噪方法,采用该去噪方法能去除二维图像信号含有的白噪声,主观评价具有很好去噪效果,能提高图像的清晰度和可识别度。本文还研究了基于小波包变换的二维信号的去噪,对指纹图像采用小波包变换进行去噪能取得很好的去噪效果。更多还原

【Abstract】 Wavelet transform is a new-style mathematic analysis tool. It is a new subject which was rapidly developed in late 1980s. The wavelet transform has the characteristic of multi-analysis and the ability to analyse partial characteristic both in the time domain and the frequency range, so it is suitable to analyze non-steady state signal and observe signal gradually from coarse to fine. The method has been used in many domains such as signal processing, image processing, pronunciation distinction, pattern recognition, quantum physics and so on. It is considered as a great breakthrough of tools and methods recently.It is inevitable to be interfered by a large amount of noise signal in the process of signal gathering and transmission. It’s a main topic to deniose and extract original signal. In practice, Donoho’s hard-thresholding and soft-thresholding algorithm is frequently used to denoising and has obtained a good effect. Discontinuity of the hard-thresholding function results in pseudo-Gibbs phenomenon of the reconstructed signal. Soft-thresholding function has good continuity but a constant deviation of the estimated value from the actual value confines its application. Thereafter all papers of this subject were centered on making some improvements based on Donoho’s thresholding method and made certain success in improving the ratio of signal to noise and denoising. In order to obtain better denoising, not only appropriate wavelet function but also the best decomposition layer must be choosed and the appropriate thresholding should be determined.The selection of thresholding affects final denoising effect directly. It’s difficult to remove the noise and reserve the primitive signal simultaneously in signal denoising. If the thresholding is too low, the denoising will be insufficient. If thresholding is too high, some weak signal will be taken as noise and denoised wrongly .Thresholding should be selected according to levels of signal.According to the definition of wavelet transform and the different characteristic of signal and the noise, a new thresholding function is proposed based on the analysis of the advantage and disadvantage of various denoising algorithms. The new threshold function has many advantages over hard-thresholding and soft-thresholding functions. It has good continuities and high-order derivatives and is convenient to treat mathematically. A novel denoising algorithm based on the new thresholding function is proposed to remove white noise mixed in one-dimensional steady signal. The white noise mixed in pronunciation signal can be effectively removed by using the algorithm and the usability and versatility is very good. The algorithm is also suitable for denoising of pronunciation signal. By using the algorithm,the white noise in which the voice signal contain can be so effectively removed that the SNR and the identifiability are greatly improved. Another denoising algorithm based on wavelet transform is proposed for two dimensional image signal processing. And by using the algorithm the white noise mixed in image signal can be effectively removed and the definition and identifiability of images can be greatly enhanceed. Denoising algorithm based on wavelet packet transform is also researched and the algorithm is for fingerprint image and the denoising effect is very satisfactory.更多还原