小波包变换用于非高斯噪声下的信号检测
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摘要
信号检测方法是信号处理的一个重要研究方向,以前的信号检测方法多是基于高斯噪声的讨论,对非高斯噪声中的信号检测研究较少。但是在雷达,通讯等领域的实际问题中,高斯噪声的假设往往难以满足实际情况。以雷达系统为例,由于大气和人工产生的各种随机性的脉冲噪声对信道的干扰,总的噪声过程将会偏离高斯分布,而呈现出拖尾分布的特性。这时,基于高斯分布假设的经典最优监测器的性能将严重恶化。
小波变换通过伸缩和平移等运算功能,对函数或信号进行多尺度细化分析,具有良好的局部化分析特性和多分辨分析特性,非常适合信号处理,成为一门兴起的信号处理技术。
本文将小波包变换用于非高斯噪声统计特性的研究,提出一种新的非高斯分布噪声下的信号检测算法。
第一章首先介绍了信号检测概况和发展以及作者的主要工作。
第二章介绍了信号检测基本理论,其中包括二元和多元假设检测,统计信号检测系统的设计思想,二元假设检测判决准则等。讲述了信号的统计检测理论是以假设检测为工具,充分利用信号和噪声的统计特性,依据不同的判决准则来设计最佳接收机的理论。
第三章介绍了小波基本理论,阐述了正交小波包的根本思想,它直接来源于多分辨分析和正交小波的构造。正交小波包除了本身具有的各种性质和应用之外,它成功地解决了小波变换固有地“高频低分辨”这一时-频分析上的缺陷。这也是本文用到的最基本的思想。
第四章主要是对经典信号检测方法在各种噪声背景下的研究。首先介绍了经典信号检测系统模型。然后对含噪声信号通过经典信号检测模型的仿真,紧接着根据仿真数据和图形对经典信号检测系统的检测性能进行了分析,最后给出结论。
第五章将小波包变换应用于信号检测中。首先阐述了非高斯噪声中检测信号用小波包变换方法的理论依据;然后通过仿真,证明
Signal dection is one of the most important research branches in the signal process. The former detection methods are mostly based on the Gaussian noise, and soldom based on non-gaussian noise. However, in radar and communication fields, the supposed gaussian noise can not meet the requirements. Taking radar system as an example, the total noises in the communication channels with various random pulse-noise interference, do not meet gaussian distribution and it trails long. Therefore, the performance of the detection system based on gaussian noise is falling down rapidly.
Wavelet transform analyses the signals or functions by the fine division which is coming from the retractility and movable characters of wavelet. It has the perfect performance of fine partly division and multiresolution, as it is fit for the signal process and becomes a new signal process technology.
In the dissertation, it puts wavelet-packet decomposition into the study on non-gaussian noise. It offers a new signal dection method under non-gaussian noise backgroud.
In the first chapter, it introduces the history of signal detection and the main work of the paper.
In the second chapter, it introduces the basic theroy of signal detection, including the duality supposed detection and multiple supposed detection, the design principle for statistic signal detection system. It also gives the theory for the best receiver design according to the different adjudging rules on the statistic character of the signal and noise.
In the third chapter, it introduces the basic theroy of the wavelet and the fundamental idea of the orhonormal wavelet-packet, which is coming from the multiresolution and the construction of orhonormal wavelet. The orhonormal wavelet-packet has many perfect characters
小波变换通过伸缩和平移等运算功能,对函数或信号进行多尺度细化分析,具有良好的局部化分析特性和多分辨分析特性,非常适合信号处理,成为一门兴起的信号处理技术。
本文将小波包变换用于非高斯噪声统计特性的研究,提出一种新的非高斯分布噪声下的信号检测算法。
第一章首先介绍了信号检测概况和发展以及作者的主要工作。
第二章介绍了信号检测基本理论,其中包括二元和多元假设检测,统计信号检测系统的设计思想,二元假设检测判决准则等。讲述了信号的统计检测理论是以假设检测为工具,充分利用信号和噪声的统计特性,依据不同的判决准则来设计最佳接收机的理论。
第三章介绍了小波基本理论,阐述了正交小波包的根本思想,它直接来源于多分辨分析和正交小波的构造。正交小波包除了本身具有的各种性质和应用之外,它成功地解决了小波变换固有地“高频低分辨”这一时-频分析上的缺陷。这也是本文用到的最基本的思想。
第四章主要是对经典信号检测方法在各种噪声背景下的研究。首先介绍了经典信号检测系统模型。然后对含噪声信号通过经典信号检测模型的仿真,紧接着根据仿真数据和图形对经典信号检测系统的检测性能进行了分析,最后给出结论。
第五章将小波包变换应用于信号检测中。首先阐述了非高斯噪声中检测信号用小波包变换方法的理论依据;然后通过仿真,证明
Signal dection is one of the most important research branches in the signal process. The former detection methods are mostly based on the Gaussian noise, and soldom based on non-gaussian noise. However, in radar and communication fields, the supposed gaussian noise can not meet the requirements. Taking radar system as an example, the total noises in the communication channels with various random pulse-noise interference, do not meet gaussian distribution and it trails long. Therefore, the performance of the detection system based on gaussian noise is falling down rapidly.
Wavelet transform analyses the signals or functions by the fine division which is coming from the retractility and movable characters of wavelet. It has the perfect performance of fine partly division and multiresolution, as it is fit for the signal process and becomes a new signal process technology.
In the dissertation, it puts wavelet-packet decomposition into the study on non-gaussian noise. It offers a new signal dection method under non-gaussian noise backgroud.
In the first chapter, it introduces the history of signal detection and the main work of the paper.
In the second chapter, it introduces the basic theroy of signal detection, including the duality supposed detection and multiple supposed detection, the design principle for statistic signal detection system. It also gives the theory for the best receiver design according to the different adjudging rules on the statistic character of the signal and noise.
In the third chapter, it introduces the basic theroy of the wavelet and the fundamental idea of the orhonormal wavelet-packet, which is coming from the multiresolution and the construction of orhonormal wavelet. The orhonormal wavelet-packet has many perfect characters
引文
(1)冉启文,谭立英.小波分析与分数傅立叶变换及应用.国防工业出版社.2002.4
(2)秦前清,杨宗凯.实用小波分析.西安电子科技大学出版社.1994:54-64,87
(3)赵瑞珍.小波理论及其在图像、信号处理中的算法研究.[西安电子科技大学博士学位论文].2001.6
(4)Guangming Shi,Ailing Ding, Licheng Jiao.A new Approach for Constructing Match Wavelet to Signal Detection. Nation Natural Science Fund of China Udner Grant No.60372047.0-7803-8647-7/04 2004 IEEE
(5)Johnstone I.M. and Silverman B.W. Wavelet threshold estimator for data with correlated noise. J.R.Statist.Soc.,series B,1997,vol.59
(6)蒋鹏.小波包分析和高阶累积量方法在探地雷达信号处理中的应用.[浙江大学博士学位论文].2004.5
(7)王成道.小波包分析和高阶累积量方法在探地雷达信号处理中的应用.[华东师范大学硕士学位论文]2001.12
(8)Philippe Ravier and Pierre-Olivier Amblard.Denoising using wavelet packets and the kurtosis application to transient detection.07803-5073-1/98/$10.00 1998 IEEE
(9)王秀芳,段玉波.小波去噪方法的仿真研究.自动化技术与应用,第23 卷第3 期.2004
(10)朱丽,娄国伟.自适应阈值的小波去噪研究.制导与引信,第24 卷第1 期.2003.3
(11)Luciano Izzo and Mario Tanda.Weak-signal diversity detection in narrowband non-Gaussian noise.0-7803-3956-8/97/$10.00 1997 IEEE
(12)孙山泽.参数统计.北京:北京大学出版社,2000:106～108.
(13)赵红怡.基于小波变换的信号检测.北方工业大学学报,第12 卷,第3 期.2000.9
(14)李玲玲,蒋栋,王广健,杨占力,李志刚.小波理论的基本思想及其发展、应用与展望.淮北煤师院学报,第23 卷第1 期.2002.3
(15)Brian M.Sadler,Georgios B.giannakis and Keh-shin Lii.Estimation and detection in non-Gaussian noise using higher order statistics.1053-587X/94$04.00 1994 IEEE
(16)Luciano Izzo,Luigi Paura, and Mario Tanda.Signal interception in non-Gaussian noise.0090-6778/92$03.00 1992 IEEE
(17)李弼程,罗建书.小波分析及其应用.电子工业出版社.2003.5
(18)杨福生.小波变换的工程分析与应用.北京科学出版社,1999:1～40,178～181
(19) Martin R D,Schiwartz S C.Robhust detection of a known signal in early Gaussian noise IEEE Trans,on IT, 1971: JT-17(l):50～56.
(20)刘有恒.信号检测与估计.北京人民邮电出版社,1989:57 70,507 511.
(21)朱华,黄辉宁,李永庆.随机信号分析.北京理工大学出版社,1990:282～286
(22)向前,林春生,龚沈光.基于小波包变换的非高斯噪声信号结构分析. 电子与信息学报,第26 卷第1 期. 2004.1. TN911.23,0177.6. 1009-5896(2004)01-0060-05
(23)罗永光, 王海云. 稳健信号处理概论[M]. 长沙: 国防科技大学出版社, 1987. 10～48, 56～68.
(24)向前,林春生,龚沈光.基于小波包变换的Robust-M 检测器. 数据采集与处理, 第18卷第3 期. 2003.9.TN 911123
(25)刘有恒. 信号检测与估计[M ]. 北京: 人民邮电出版社, 1989. 507～547.
(26)奏前清,杨宗凯.实用小波分析.西安:西安电子科技大学出版社.1994:54～64,87
(27)Zhou J.,Civio D.L.and Silander J.A.A wavelet transform method to merge landsat TM and SPOT Panchlomatic data.International Joumal of Remote Sensing,1998,19(4):743～757
(28)王雷,罗传翼,程桂芬.基于小波变换消除信号噪声的研究.现代电子技术.2001
(29)赵瑞珍,宋国乡.一种基于小波变换的白噪声消噪方法的改进.西安电子科技大学学报.2000,27(5):619～622
(30)赵瑞珍,宋国乡,屈汉章.重构小波系数的分段三次样条插值新算法.信号处理. 2001,17(3):242～246
(31)程俊,张璞,戴善荣等.小波变换用于信号突变的检测。通信学报.1995,5, 16(3):96～104
(32)Vetterli M.and HerleyC,Wavelets and filter banks:theory and design.IEEE Trans.on SP.,1992.9,40(9):2207～2232
(33)Strang G.and Nguyen T. Wavelet and filter banks.Wellesley Cambridge press, 1996
(34)Unser M.,Therenaz P. and Aldroubi A.Shift-orthogonal wavelet bases.IEEE Trans.on SP.,1998.7,46(7):1827～1836
(35) Unser M.,Therenaz P. and Aldroubi A.Shift-orthogonal wavelet bases using splines.IEEE Signal Processing Lett.,1996.3,3(3):85～88
(36)冯象初.偏微分方程的小波分析方法.[西安电子科技大学博士学位论文],1998.10
(37)Arneodo A.,Bacry E.and Muzy J.F.Solving the inverse fractal problem from wavelet analysis.Euronhvsics Letters.1 995.25(7):484～497
(38)Zhang X D and Zhang Y S.FIR system identification using higher order cumulants alone.IEE Trans on Signal Processing,1994,42(10):2854～2858
(39)Mareum,J.I. A Statistical Theory of Detection by Pulsed Radar and Mathematical
(2)秦前清,杨宗凯.实用小波分析.西安电子科技大学出版社.1994:54-64,87
(3)赵瑞珍.小波理论及其在图像、信号处理中的算法研究.[西安电子科技大学博士学位论文].2001.6
(4)Guangming Shi,Ailing Ding, Licheng Jiao.A new Approach for Constructing Match Wavelet to Signal Detection. Nation Natural Science Fund of China Udner Grant No.60372047.0-7803-8647-7/04 2004 IEEE
(5)Johnstone I.M. and Silverman B.W. Wavelet threshold estimator for data with correlated noise. J.R.Statist.Soc.,series B,1997,vol.59
(6)蒋鹏.小波包分析和高阶累积量方法在探地雷达信号处理中的应用.[浙江大学博士学位论文].2004.5
(7)王成道.小波包分析和高阶累积量方法在探地雷达信号处理中的应用.[华东师范大学硕士学位论文]2001.12
(8)Philippe Ravier and Pierre-Olivier Amblard.Denoising using wavelet packets and the kurtosis application to transient detection.07803-5073-1/98/$10.00 1998 IEEE
(9)王秀芳,段玉波.小波去噪方法的仿真研究.自动化技术与应用,第23 卷第3 期.2004
(10)朱丽,娄国伟.自适应阈值的小波去噪研究.制导与引信,第24 卷第1 期.2003.3
(11)Luciano Izzo and Mario Tanda.Weak-signal diversity detection in narrowband non-Gaussian noise.0-7803-3956-8/97/$10.00 1997 IEEE
(12)孙山泽.参数统计.北京:北京大学出版社,2000:106～108.
(13)赵红怡.基于小波变换的信号检测.北方工业大学学报,第12 卷,第3 期.2000.9
(14)李玲玲,蒋栋,王广健,杨占力,李志刚.小波理论的基本思想及其发展、应用与展望.淮北煤师院学报,第23 卷第1 期.2002.3
(15)Brian M.Sadler,Georgios B.giannakis and Keh-shin Lii.Estimation and detection in non-Gaussian noise using higher order statistics.1053-587X/94$04.00 1994 IEEE
(16)Luciano Izzo,Luigi Paura, and Mario Tanda.Signal interception in non-Gaussian noise.0090-6778/92$03.00 1992 IEEE
(17)李弼程,罗建书.小波分析及其应用.电子工业出版社.2003.5
(18)杨福生.小波变换的工程分析与应用.北京科学出版社,1999:1～40,178～181
(19) Martin R D,Schiwartz S C.Robhust detection of a known signal in early Gaussian noise IEEE Trans,on IT, 1971: JT-17(l):50～56.
(20)刘有恒.信号检测与估计.北京人民邮电出版社,1989:57 70,507 511.
(21)朱华,黄辉宁,李永庆.随机信号分析.北京理工大学出版社,1990:282～286
(22)向前,林春生,龚沈光.基于小波包变换的非高斯噪声信号结构分析. 电子与信息学报,第26 卷第1 期. 2004.1. TN911.23,0177.6. 1009-5896(2004)01-0060-05
(23)罗永光, 王海云. 稳健信号处理概论[M]. 长沙: 国防科技大学出版社, 1987. 10～48, 56～68.
(24)向前,林春生,龚沈光.基于小波包变换的Robust-M 检测器. 数据采集与处理, 第18卷第3 期. 2003.9.TN 911123
(25)刘有恒. 信号检测与估计[M ]. 北京: 人民邮电出版社, 1989. 507～547.
(26)奏前清,杨宗凯.实用小波分析.西安:西安电子科技大学出版社.1994:54～64,87
(27)Zhou J.,Civio D.L.and Silander J.A.A wavelet transform method to merge landsat TM and SPOT Panchlomatic data.International Joumal of Remote Sensing,1998,19(4):743～757
(28)王雷,罗传翼,程桂芬.基于小波变换消除信号噪声的研究.现代电子技术.2001
(29)赵瑞珍,宋国乡.一种基于小波变换的白噪声消噪方法的改进.西安电子科技大学学报.2000,27(5):619～622
(30)赵瑞珍,宋国乡,屈汉章.重构小波系数的分段三次样条插值新算法.信号处理. 2001,17(3):242～246
(31)程俊,张璞,戴善荣等.小波变换用于信号突变的检测。通信学报.1995,5, 16(3):96～104
(32)Vetterli M.and HerleyC,Wavelets and filter banks:theory and design.IEEE Trans.on SP.,1992.9,40(9):2207～2232
(33)Strang G.and Nguyen T. Wavelet and filter banks.Wellesley Cambridge press, 1996
(34)Unser M.,Therenaz P. and Aldroubi A.Shift-orthogonal wavelet bases.IEEE Trans.on SP.,1998.7,46(7):1827～1836
(35) Unser M.,Therenaz P. and Aldroubi A.Shift-orthogonal wavelet bases using splines.IEEE Signal Processing Lett.,1996.3,3(3):85～88
(36)冯象初.偏微分方程的小波分析方法.[西安电子科技大学博士学位论文],1998.10
(37)Arneodo A.,Bacry E.and Muzy J.F.Solving the inverse fractal problem from wavelet analysis.Euronhvsics Letters.1 995.25(7):484～497
(38)Zhang X D and Zhang Y S.FIR system identification using higher order cumulants alone.IEE Trans on Signal Processing,1994,42(10):2854～2858
(39)Mareum,J.I. A Statistical Theory of Detection by Pulsed Radar and Mathematical