基于小波变换的超声检测信号去噪方法研究
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摘要
实际应用中接收到的超声检测信号不仅含有大量有用信息,同时还夹杂着各种干扰信号(噪声),而这些干扰信号的存在严重影响了信号的本来面目,不利于信号的分析和进一步处理。因此,在超声检测信号的预处理过程中对噪声加以消除或减小,是十分必要和重要的。
小波分析是目前国际上公认的信号信息获取与处理领域的高新技术,是信号处理的前沿课题,并在实际中得到了广泛的应用。本文根据小波的基本理论,提出了一些新的小波去噪算法,并将其应用到超声检测信号的去噪中,进而拓宽了小波的应用范围。主要工作包括:
1.研究小波阈值去噪的各种方法,分析传统软阈值法和硬阈值法的特点,并在标准软硬阈值折中法的基础上,提出了一种软硬阈值改良折中法。该方法与标准软硬阈值折中法相比,其阈值函数具有更加灵活多变的形式,便于进行各种数学处理;与传统软阈值法和硬阈值法相比,它克服了硬阈值函数不连续的缺点,减小了软阈值函数中的估计小波系数与分解小波系数之间存在的恒定偏差。仿真实验结果表明,该改良方法的去噪性能优于传统软阈值法、硬阈值法和标准软硬阈值折中法。
2.研究了粒子群优化算法的特性,将其应用于小波阈值去噪方法中,对阈值进行寻优,并使用garrote阈值函数量化小波分解系数。而garrote阈值函数既克服了硬阈值函数的不连续性,也减小了软阈值函数存在的恒定偏差。最后通过仿真实验,证明了该方法的有效性。
3.按照小波包的基本理论,并根据噪声与信号在各频带上的小波包系数具有不同特征的特点,将Stein无偏似然估计阈值、贝叶斯阈值、固定形式阈值与滑动极大极小准则阈值结合,应用到小波包阈值去噪中。仿真结果表明,该方法具有较好的去噪效果。
总而言之,研究小波的基本理论,提出改进方法并应用到新的领域,具有重要的理论意义和实用价值。
In practical use, the ultrasonic testing signal received not only includes much useful information, but also has various interference signals (these are noises) in it, and the interference signal affects the real ultrasonic testing signal heavily, which goes against the analysis and farther treatment of ultrasonic testing signal. Therefore, it is quite necessary and important that eliminating or decreasing noise during the pretreatment of ultrasonic testing signal.
Wavelet analysis is internationally acknowledged high technology in the fields of information obtained and processed at present, and it is the forward topic of signal processing, also it is used widely in practical. Based on the wavelet theory, this article proposed several new wavelet denoising methods, which were used in the denoising area of ultrasonic testing signal, thus the application range of wavelet was widen. The main works of this article are as follows:
1. The wavelet threshold denoising methods were discussed emphatically, and the characteristics of two traditional wavelet shrinkage methods, which referred to soft-threshold and hard-threshold respectively, were analyzed in wavelet domain, then a modified compromise threshold method was proposed on the basis of the standard compromise threshold method. Compared with the standard compromise threshold method, the threshold function of the modified method has more flexible form, which is convenient for several kinds of mathematical disposals; compared with the two traditional wavelet shrinkage methods, it overcomes the shortcoming of discontinuity of hard-threshold and decreases the fixed bias between estimated wavelet coefficients and decomposed wavelet coefficients of soft-threshold. The simulation results show that the modified method is better than the methods, which contain soft-threshold method, hard-threshold method and the standard compromise threshold method.
2. After studied the characteristics of Particle Swarm Optimization, Particle Swarm Optimization was used in wavelet domain to optimize the thresholds, and garrote shrinkage function was used to process wavelet decomposition coefficients, which overcame the shortcoming of discontinuity of hard-threshold and decreased the fixed bias between estimated wavelet coefficients and decomposed wavelet coefficients of soft-threshold. The simulation results show the validity of this new method.
3. Introduce the basic theories of wavelet packet analysis in detail. And according to the feature that the wavelet coefficients of signals and noises on each scale had different characteristic, SURE threshold, Bayesian threshold, fixed form threshold and the moving minimax threshold were combined during wavelet packet threshold de-noising. Simulation results show that the proposed method indeed has better de-noising effect.
In a word, study basic theories of wavelet, and apply into new field with improved methods. This topic has important theoretical significance and practical value.
小波分析是目前国际上公认的信号信息获取与处理领域的高新技术,是信号处理的前沿课题,并在实际中得到了广泛的应用。本文根据小波的基本理论,提出了一些新的小波去噪算法,并将其应用到超声检测信号的去噪中,进而拓宽了小波的应用范围。主要工作包括:
1.研究小波阈值去噪的各种方法,分析传统软阈值法和硬阈值法的特点,并在标准软硬阈值折中法的基础上,提出了一种软硬阈值改良折中法。该方法与标准软硬阈值折中法相比,其阈值函数具有更加灵活多变的形式,便于进行各种数学处理;与传统软阈值法和硬阈值法相比,它克服了硬阈值函数不连续的缺点,减小了软阈值函数中的估计小波系数与分解小波系数之间存在的恒定偏差。仿真实验结果表明,该改良方法的去噪性能优于传统软阈值法、硬阈值法和标准软硬阈值折中法。
2.研究了粒子群优化算法的特性,将其应用于小波阈值去噪方法中,对阈值进行寻优,并使用garrote阈值函数量化小波分解系数。而garrote阈值函数既克服了硬阈值函数的不连续性,也减小了软阈值函数存在的恒定偏差。最后通过仿真实验,证明了该方法的有效性。
3.按照小波包的基本理论,并根据噪声与信号在各频带上的小波包系数具有不同特征的特点,将Stein无偏似然估计阈值、贝叶斯阈值、固定形式阈值与滑动极大极小准则阈值结合,应用到小波包阈值去噪中。仿真结果表明,该方法具有较好的去噪效果。
总而言之,研究小波的基本理论,提出改进方法并应用到新的领域,具有重要的理论意义和实用价值。
In practical use, the ultrasonic testing signal received not only includes much useful information, but also has various interference signals (these are noises) in it, and the interference signal affects the real ultrasonic testing signal heavily, which goes against the analysis and farther treatment of ultrasonic testing signal. Therefore, it is quite necessary and important that eliminating or decreasing noise during the pretreatment of ultrasonic testing signal.
Wavelet analysis is internationally acknowledged high technology in the fields of information obtained and processed at present, and it is the forward topic of signal processing, also it is used widely in practical. Based on the wavelet theory, this article proposed several new wavelet denoising methods, which were used in the denoising area of ultrasonic testing signal, thus the application range of wavelet was widen. The main works of this article are as follows:
1. The wavelet threshold denoising methods were discussed emphatically, and the characteristics of two traditional wavelet shrinkage methods, which referred to soft-threshold and hard-threshold respectively, were analyzed in wavelet domain, then a modified compromise threshold method was proposed on the basis of the standard compromise threshold method. Compared with the standard compromise threshold method, the threshold function of the modified method has more flexible form, which is convenient for several kinds of mathematical disposals; compared with the two traditional wavelet shrinkage methods, it overcomes the shortcoming of discontinuity of hard-threshold and decreases the fixed bias between estimated wavelet coefficients and decomposed wavelet coefficients of soft-threshold. The simulation results show that the modified method is better than the methods, which contain soft-threshold method, hard-threshold method and the standard compromise threshold method.
2. After studied the characteristics of Particle Swarm Optimization, Particle Swarm Optimization was used in wavelet domain to optimize the thresholds, and garrote shrinkage function was used to process wavelet decomposition coefficients, which overcame the shortcoming of discontinuity of hard-threshold and decreased the fixed bias between estimated wavelet coefficients and decomposed wavelet coefficients of soft-threshold. The simulation results show the validity of this new method.
3. Introduce the basic theories of wavelet packet analysis in detail. And according to the feature that the wavelet coefficients of signals and noises on each scale had different characteristic, SURE threshold, Bayesian threshold, fixed form threshold and the moving minimax threshold were combined during wavelet packet threshold de-noising. Simulation results show that the proposed method indeed has better de-noising effect.
In a word, study basic theories of wavelet, and apply into new field with improved methods. This topic has important theoretical significance and practical value.
引文
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2.杨宗凯.小波去噪及其在信号检测中的应用[J].华中理工大学学报, 1997, 25(2): 1-4
3.马丽萍,石炎福,余华瑞.小波分析及其在化工信号分析处理中的应用及展望[J].化工进展, 2005, 24(2): 147-153
4. Michael T Johnson, Yuan Xiaolong, Yao Ren.Speech signal enhancement through adaptive wavelet thresholding[J]. Speech Communication, 2007, 49: 123-133
5.葛馨远,孙中伟,许刚.基于小波域隐Markov树模型及重要性修正的绝缘子红外图像去噪研究[J].电网技术, 2007, 31(2): 3-7
6.董卫军,樊养余,周明全.基于多小波变换的图像去噪[J].计算机应用与软件, 2007, 24(12): 32-33
7.樊亚军,曹蔚,王蕊.利用改进的小波阈值算法进行图像消噪处理[J].西安工业大学学报, 2007, 27(6): 567-589
8. S Bacchelli, S Papi.Statistically based multiwavelet denoising[J]. Journal of Computational and Applied Mathematics, 2006, 1-9
9. S Grace Chang, Bin Yu, Martin Vetterli. Adaptive wavelet threshold for image denoising and compression[J]. IEEE Transactions on Image Processing, 2000, 9(9): 1532-1546
10.张宗平,刘贵忠.基于小波的视频图像压缩研究进展[J].电子学报, 2002, 30(6): 883-889
11.袁静,冯前进,陈武凡等.基于小波分解的快速分形图像压缩算法[J].中国图象图形学报, 2003, 8(4): 392-397
12.张松,蔡方凯,董凯宁.基于嵌入零树小波算法的磁共振图像压缩研究[J].通信技术, 2007, 40(12): 400-402
13.郭敏如,刘慧.基于小波变换的遥感图像融合算法[J].北京化工大学学报, 2007, 34: 126-128
14.黄彩霞,陈家新.基于小波系数区域相似度的医学图像融合[J].计算机应用研究, 2008, 25(1): 274-276
15.张明源,王宏力,陈国栋.基于小波分析的多源图像融合去云技术研究[J].传感器与微系统, 2007, 26(11): 19-21
16.萨义德V瓦塞编.现代数字信号处理与噪声降低[M]:第3版.邱天爽等译.北京:电子工业出版社, 2007. 17-26
17. Robert E, Green Jr.Non-contact ultrasonic techniques[J]. Ultrasonics, 2004, 42: 9-16
18. Margaret S Greenwood, Judith A Bamberger. Ultrasonic sensor to measure the density of a liquid or slurry during pipeline transport[J]. Ultrasonics, 2002, 40: 413-417
19. Gregorio Andria, Filippo Attivissimo, Nicola Giaquinto. Digital signal processing trchniques for accurate ultrasonic sensor measurement[J]. Measurement, 2001, 30: 105-114
20.毛捷,简晓明,李明轩,等.信号处理在超声检测中的应用[J].应用声学, 2000, 19(3): 45-47
21.胡广书.现代信号处理教程[M].北京:清华大学出版社, 2004. 52-60, 72-85, 97-103, 239-266, 309-313
22.施克仁.超声检测信号处理[J].无损检测, 1994, 16(5): 141-144
23. M Thavasimuthu, C Rajagopalan, P Kayanasundaram, et al. Improving the evaluation sensitivity of an ultrasonic pulse echo technique using a neural network classifier[J]. NDT&E International, 1996, 29(3): 175-179
24. Liu Zhenqing, Lu Mingda, Wei Moan. Structure noise reduction of ultrasonic signals using artifitial neural network adaptive filtering[J]. Ultrasonics, 1997, 35: 325-328
25. R Vicen, R Gil, P Jarabo,M Rosa, et al. Non-linear filtering of ultrasonic signals using neural networks[J]. Ultrasonics, 2004, 42: 355-360
26.董长虹,高志,余啸海. Matlab小波分析工具箱原理与应用[M].北京:国防工业出版社, 2004.3-18
27.孙延奎.小波分析及其应用[M].北京:机械工业出版社, 2005. 31-52, 157-175, 219-235, 245-257
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