基于小波变换的地震勘探信号处理技术研究
|
摘要
提高地震信号的信噪比是提高地震信号分辨率的先决条件,要提高地震资料的信噪比,需要去除地震资料中的噪声。地震勘探信号中的噪声主要有两种:相干噪声和随机噪声。相干噪声在时间上具有规律性,可以依据这些规律加以去除,一般相干噪声主要包括面波、多次波、折射鸣震等。而随机噪声没有统一的规律,它包括环境噪声、测量误差、地面微震等。本文主要研究了随机噪声的去除。在很多地震信号去噪的方法中都用到傅立叶变换和短时傅立叶变换,但傅立叶变换只对于确知信号和平稳随机过程有显著的意义,而实际信号往往是时变信号、非平稳过程,了解它们的局部特性常常是很重要的,短时傅立叶变换又不能同时兼顾时间分辨率和频率分辨率。近年来,小波变换在地震信号处理中的应用一直是人们研究的一大热点,己取得了令人瞩目的成果。因为它在时域和频域都具有很好的局部化性质,可以将信号所携带的信息分解到任意细节加以分析,并且信号和噪声在小波变换的细节信息具有截然不同的特性,因此可将其用于地震信号去噪,以更为准确地区分有效信号和噪声,在最大限度去除噪声的同时,尽可能保留有效信号。本论文主要利用离散二进小波变换对地震信号进行分析和去噪处理。
论文首先介绍了地震波场的特点,对地震信号中主要噪声类型进行介绍,并针对其特点介绍了目前使用的去除相干噪声和随机噪声的各种方法,并简要分析了各方法的优缺点。论文对小波变换基本原理做了较为详细的介绍,讨论了小波变换的基本原理及常用小波函数。
针对信号和噪声在小波变换下模极大值在各尺度上不同的传播特性,利用小波变换模极大值进行信号去噪和重构。基于小波变换模极大值的地震信号去噪方法能够较好地去除地震信号中随机噪声,且在不同尺度上能够更精细地区分信号和噪声,使得在去除高频噪声的同时,可以尽可能多地保留有效的高频信息。由于白噪声具有负的奇异性,且其幅度和稠密度随尺度增加而减少,因此如果某个信号的小波变换局部模极大值的幅度及稠密度随尺度减小而快速增大,表明该处的奇异性主要由噪声控制,在去噪时应予去除。因此文中采用了一种有噪声控制的模极大值的算法来进行消噪,取得了较好的处理结果。
论文介绍了常规小波域阈值去噪处理方法,并分析了小波阈值去噪的性能。小波阈值去噪虽然能够去除信号中随机噪声,提高信噪比,但在实际应用中单独使用常规的小波域阈值去噪,效果有时还不能令人满意。因此文中采用了一种结合软硬阈值的加权阈值去噪方法,经实际地震剖面处理验证,该方法比直接应用常规的小波域阈值去噪有更好的处理效果,对信号的逼近程度高,并能抑制Gibbs振荡现象。
论文针对小波变换模极大值的信号去噪方法存在算法稳定性较差及计算量很大的问题,讨论了另一种基于小波变换在不同尺度传播特性的去噪方法——基于小波变换尺度间相关性去噪方法。通过把尺度间的小波系数进行相关处理,则有效信号的小波系数被相关加强,而噪声的小波系数被相关减弱,以此来实现信噪分离。论文分析了同一尺度下的迭代过程、不同类型和不同信噪比下含噪信号的去噪效果,并研究了一种改进的尺度相关去噪算法,经对实际地震信号处理结果表明了其有效性。
在论文的最后,总结了本文所做的工作和成果,指出了研究的不足之处和将来的研究方向。
The prerequisite condition of improving the resolving power is to improve the SNR of signal, which need to remove the noise from seismic data. There are two kind of noise in seismic data: coherent noises and random noises. Coherent noises are disciplinary and can be removed according to the rules. Usually, coherent noises comprise of surface wave, multiple wave, refraction and ringing. Random noises have uniform rules and they comprise of circumstance noise, measurement error and ground microseism. The paper discusses the random noise removing.
Fourier transformation and short Fourier transformation are used in many seismic data noise removing. But Fourier transformation is applicable to deterministic signal and stationary and related stochastic processes. The practical signal usually is time-varied and non-stationary and it is important to comprehend its local characteristic. Short Fourier transform can’t consider time resolution and frequency resolution. Recently, wavelet transform has become hotspot in seismic signal process and many fruits have been acquired. Wavelet transform has good local characteristic in time and frequency domain and can decomposes arbitrary detail of signal.
The detail characteristic of signal and noise are different during wavelet transform, which can be used to remove noise of seismic data in order to distinguish effective signal and noise. The effective signal can be reserved when the noises are removed as far as possible. The dyadic discrete wavelet transform is used to analyze seismic data and remove noise.
The characteristic of seismic wave scene is introduced first, then the main noise styles in seismic data are discussed. The noise removing method of coherent noise and random noise are also introduced with their characteristics. Then, the paper discusses the discipline of wavelet transform and several wavelet functions. As the different propagation characteristic of signal and noise on different scales of modules maxima, the signal can be de-noised and reconstructed. The method can remove random noise in seismic data preferably, and the signal and noise can be distinguished on different scales, which can reserve the effective high frequency information as far as when removing high frequency noise. The white noise has native singular, its amplitude denseness decrease with scales, so if the amplitude and denseness of local modules maxima for a signal decrease quickly with scales, it indicates that the singular of this point is controlled by noise and should be removed. Therefore, a modules maxima algorithm controlled by noise is adopted in the paper to remove noise and acquires prefer results.
The general de-noising method based on wavelet threshold is also introduced and its performance is analyzed. Although the threshold method can remove random noise, the effect couldn’t turn up trumps. So the weighted threshold combined soft and hard-threshold is adopted in the paper, the process results demonstrate that it can approach to signal preferably and restrain Gibbs oscillation.
The noise removing based on modules maxima of wavelet transform has the problem such as bad stability and large calculation, so inter-scale relativity de-noising method is discussed. The wavelet coefficients are enhanced relatively by correlating the inter-scale coefficients to distinguish the signal and noise. The paper analyzes the noise removing effect such as iterative course on same scale, different style and SNR, and an improved inter-scale relativity de-noising algorithm is discussed. The results demonstrate its effectiveness.
At last, the work and harvest is summarized, the deficiency and future direction are also indicated.
论文首先介绍了地震波场的特点,对地震信号中主要噪声类型进行介绍,并针对其特点介绍了目前使用的去除相干噪声和随机噪声的各种方法,并简要分析了各方法的优缺点。论文对小波变换基本原理做了较为详细的介绍,讨论了小波变换的基本原理及常用小波函数。
针对信号和噪声在小波变换下模极大值在各尺度上不同的传播特性,利用小波变换模极大值进行信号去噪和重构。基于小波变换模极大值的地震信号去噪方法能够较好地去除地震信号中随机噪声,且在不同尺度上能够更精细地区分信号和噪声,使得在去除高频噪声的同时,可以尽可能多地保留有效的高频信息。由于白噪声具有负的奇异性,且其幅度和稠密度随尺度增加而减少,因此如果某个信号的小波变换局部模极大值的幅度及稠密度随尺度减小而快速增大,表明该处的奇异性主要由噪声控制,在去噪时应予去除。因此文中采用了一种有噪声控制的模极大值的算法来进行消噪,取得了较好的处理结果。
论文介绍了常规小波域阈值去噪处理方法,并分析了小波阈值去噪的性能。小波阈值去噪虽然能够去除信号中随机噪声,提高信噪比,但在实际应用中单独使用常规的小波域阈值去噪,效果有时还不能令人满意。因此文中采用了一种结合软硬阈值的加权阈值去噪方法,经实际地震剖面处理验证,该方法比直接应用常规的小波域阈值去噪有更好的处理效果,对信号的逼近程度高,并能抑制Gibbs振荡现象。
论文针对小波变换模极大值的信号去噪方法存在算法稳定性较差及计算量很大的问题,讨论了另一种基于小波变换在不同尺度传播特性的去噪方法——基于小波变换尺度间相关性去噪方法。通过把尺度间的小波系数进行相关处理,则有效信号的小波系数被相关加强,而噪声的小波系数被相关减弱,以此来实现信噪分离。论文分析了同一尺度下的迭代过程、不同类型和不同信噪比下含噪信号的去噪效果,并研究了一种改进的尺度相关去噪算法,经对实际地震信号处理结果表明了其有效性。
在论文的最后,总结了本文所做的工作和成果,指出了研究的不足之处和将来的研究方向。
The prerequisite condition of improving the resolving power is to improve the SNR of signal, which need to remove the noise from seismic data. There are two kind of noise in seismic data: coherent noises and random noises. Coherent noises are disciplinary and can be removed according to the rules. Usually, coherent noises comprise of surface wave, multiple wave, refraction and ringing. Random noises have uniform rules and they comprise of circumstance noise, measurement error and ground microseism. The paper discusses the random noise removing.
Fourier transformation and short Fourier transformation are used in many seismic data noise removing. But Fourier transformation is applicable to deterministic signal and stationary and related stochastic processes. The practical signal usually is time-varied and non-stationary and it is important to comprehend its local characteristic. Short Fourier transform can’t consider time resolution and frequency resolution. Recently, wavelet transform has become hotspot in seismic signal process and many fruits have been acquired. Wavelet transform has good local characteristic in time and frequency domain and can decomposes arbitrary detail of signal.
The detail characteristic of signal and noise are different during wavelet transform, which can be used to remove noise of seismic data in order to distinguish effective signal and noise. The effective signal can be reserved when the noises are removed as far as possible. The dyadic discrete wavelet transform is used to analyze seismic data and remove noise.
The characteristic of seismic wave scene is introduced first, then the main noise styles in seismic data are discussed. The noise removing method of coherent noise and random noise are also introduced with their characteristics. Then, the paper discusses the discipline of wavelet transform and several wavelet functions. As the different propagation characteristic of signal and noise on different scales of modules maxima, the signal can be de-noised and reconstructed. The method can remove random noise in seismic data preferably, and the signal and noise can be distinguished on different scales, which can reserve the effective high frequency information as far as when removing high frequency noise. The white noise has native singular, its amplitude denseness decrease with scales, so if the amplitude and denseness of local modules maxima for a signal decrease quickly with scales, it indicates that the singular of this point is controlled by noise and should be removed. Therefore, a modules maxima algorithm controlled by noise is adopted in the paper to remove noise and acquires prefer results.
The general de-noising method based on wavelet threshold is also introduced and its performance is analyzed. Although the threshold method can remove random noise, the effect couldn’t turn up trumps. So the weighted threshold combined soft and hard-threshold is adopted in the paper, the process results demonstrate that it can approach to signal preferably and restrain Gibbs oscillation.
The noise removing based on modules maxima of wavelet transform has the problem such as bad stability and large calculation, so inter-scale relativity de-noising method is discussed. The wavelet coefficients are enhanced relatively by correlating the inter-scale coefficients to distinguish the signal and noise. The paper analyzes the noise removing effect such as iterative course on same scale, different style and SNR, and an improved inter-scale relativity de-noising algorithm is discussed. The results demonstrate its effectiveness.
At last, the work and harvest is summarized, the deficiency and future direction are also indicated.
引文
[1]王有新,王延光.地震勘探技术概述[J].油气地球物理,Vol.5,No.12,2007:1-9.
[2].陆基孟.地震勘探原理.北京:石油大学出版社,1993.
[3]张德忠.陆上石油地震勘探技术进步50年[J].石油地球物理勘探,Vol.35.No.5,2000:545-558.
[4]杨建广,吕绍林.地球物理信号处理技术的研究及进展[J].地球物理学进展,Vol.17,No.1,2002:171-175.
[5]付燕.人工地震信号去噪方法研究[D].西安:西北工业大学出版社,2002.
[6]张军华,吕宁,田连玉,陆文志,钟磊.地震资料去噪方法技术综合评述[J].地球物理学进展,Vol.21,No.2,2006:546-553.
[7]李鸣社.地震勘探资料数字处理[M].中国矿业大学出版社,1989.
[8]文莉,刘正士,葛运建.小波去噪的几种方法[J].合肥工业大学学报(自然科学版),2002,25(2):167-172。
[9]蒋录全,何光明.小波理论及其在地震勘探中的应用[J].地质科技情报,Vol.14 (1),1995,892-893.
[10]赵玉宝.小波变换在地震信号去噪中的应用研究[D].中南大学硕士论文,2005.
[11]黄力军.浅谈地震信号中的噪声及去除方法[J].内蒙古石油化工,No.4,2008,31-34.
[12]梁学章,何甲兴,王新民,李强.小波分析[M].北京:国防工业出版社,2005.
[13]程正兴.小波分析算法与应用[M].西安:西安交通大学出版社,1998.
[14]裴正林.小波理论及其在地震数据处理中的应用[J].地球物理学进展,Vol.17,No.3,2002:486-490.
[15]高静怀,汪文秉,朱光明等.地震资料处理中小波函数的选取研究[J].地球物理学报,39(3),1996:392～400.
[16]秦前清,杨宗凯.实用小波分析[M].西安:西安电子科技大学出版社,1998.
[17]刘春生,张晓春.实用小波分析[M].徐州:中国矿业大学出版社,2002.
[18]岑翼刚,岑丽辉,孙德宝.信号Lipschitz奇异性的计算与分析[J].计算机工程与应用,Vol.18,2004,35-37.
[19]覃太贵,张学英,羿旭明.小波变换在信号奇异性检测中的应用[J].数学杂志,24(3),2004:323-326.
[20]张小飞,徐大专,齐泽锋.基于小波变换奇异信号检测的研究[J].系统工程与电子技术,2003,25(7):814-816.
[21]戴建新,郦志新,宋洪雪.基于小波的信号Lipschitz指数分析和应用[J].南京邮电大学学报(自然科学版),Vol.28,No.6,2008:69-73.
[22] Cvetkovic Z. Vetterli M. Discrete-time wavelet extreme representation: Design and consistent reconstruction [J]. IEEE Trans Signal Processing.1995, 43(3): 681-693.
[23] Liu G Z, Zhang Z M. Iterative shaping reconstruction algorithm based on the modules maxima of signal’s dyadic wavelet transform [J]. Progress in Natural Science, 2000, 10(8): 660-664.
[24] Mallat S, Zhang S. Characterization of signal from multi-scale edges[J]. IEEE Trans Pattern Analysis and Machine Intelligence, 1992, 14(7): 710-732.
[25] J.Morlet, G.Arens, E.Fourgeau and D.Giard. Wave propagation and sampling theory-part I: Complex signal and scattering multilayered media [J].Geophysi cs, 47(2), 1982:203-221.
[26] Mallat S. Zero-crossings of a wavelet transform. IEEE Trans Information Theory [J]. 37(4), 1991:1019-1033.
[27]陈德智,唐磊.由小波变换的模极大值快速重构信号[J].电子学报,26(9),1998: 82-85.
[28]廖国勇,徐长友.一种快速重构信号的方法[J].华中科技大学学报,30(8),2002:98-100.
[29]蔡汉添,宋勇.关于子波变换局部极大值信号重构的交替投影算法[J].数据采集与处理,1998,Vol.13(2):112-116.
[30]张茁生,刘贵忠,刘峰.一种新的信号二进小波变换模极大值重构信号的迭代算法[J].中国科学,Vol.33,No.6,2003:545-553.
[31]何永红,文鸿雁,靳鹏伟.一种基于小波模极大值去噪的改进算法[J].大地测量与地球动力学,Vol.27,No.2,2007:94-98.
[32]韩民,田岚.基于Hermite插值的小波变换模极大值重构信号快速算法[J].系统仿真学报,Vol.11,No.2,12005:626-2 619.
[33]张兆宁,董肖红,潘云峰.基于小波变换模极大值去噪方法的改进[J].电力系统及其自动化学报.Vol.17,No.2,2005:9-12.
[34] Hsung Taichiu, Lun Daniel Pakkong, Siu Wanchi. Denoising by singularity detect ion [J]. IEEE T ranson Signal Processing, 1999, 47 (11): 3139-3144.
[35]王和平,康景利.一种基于小波模极大值的信号去噪算法[J].系统工程与电子技术,Vol.27,No.11,2005:1876-1877.
[36]张军萍,蔡汉添.基于子波变换局部极大值的信号去噪新算法[J].电路与系统学报,Vol.2(2),1997:31-34.
[37]顾意农,张志宏,吴正国,郑学铃.基于小波变换模极大值恢复的信号消噪方法[J]海军工理大学学报,13(2):25-32,2001
[37] David L. Donoho. De-Noising by Soft-Thresholding [J]. IEEE TRANS. ON INFORMATION THEORY, VOL. 41, NO. 3, 1995:613-627.
[38]袁兰敬.小波变换在信号去噪中的应用[D].中国地质大学(北京),硕士论文,2008.
[39] BAKHTAZAD A, PALAZOGLU A, ROMANGOL I J A. Process data denoising usingwavelet transform[J]. Telligent Data Analysis, Vol.3 (4), 1999: 267-285.
[40] XU Yansun. Wavelet transform domain filters: a spatially selective noise filtration technique [J]. IEEE Trans on Image Processing, Vol.3 (6), 1994 : 747 - 758.
[41]夏洪瑞,朱勇,周开明.小波变换及其在去噪中的应用[J].石油地球物理勘探,Vol.29 (3),1994:274～285.
[42]刘庆普,胡留军.地震数据去噪中的小波方法[J].哈尔滨工程大学学报,Vol.23,NO.4,2002:86-90.
[43] ZhangLei, Pan Quan, et al. On the determination of threshold in threshold based denoising by wavelet transformation [J]. Acta Electronic a Sinica, Vol.29 (3) , 2001: 400-403.
[44] Azzalini A , Farge M , Schneider K. Nonlinear wavelet thresholding: A recursive method to determine the optimal denoising threshold [J]. Appl. Comput. Harmon. A nal, 2005 (18):177- 185.
[45]李华.小波理论分析及其在地震信号处理中的应用研究[D].成都:成都理工学院,2000.
[46]张媛玲.小波分析在地震勘探资料处理中的应用[D].沈阳:沈阳工业大学,2001.
[47]张吉先,钟秋海,戴亚平.小波门限消噪法应用中分解层数及阈值的确定[J].中国电机工程学报,Vol24,No.2,2004:118-122.
[48]潘泉,戴冠中,张洪才.具有理论阈值的小波滤波方法[J].宇航学报,Vol.19(4),1998:81-85.
[49]刘永峰,武俊,王晓光.一种基于小波阈值去噪的改进方法[J].电脑知识与技术,2006:154-155.
[50]陶红艳,秦华峰,余成波.基于改进阈值函数的小波域去噪算法的研究[J].压电与声光,Vol.30,No.1,2008:93-95.
[51]侯锐锋.小波变换在地震资料随机噪声去除中的应用[D].成都理工大学硕士论文,2009.
[52] CHAN G S, YU B, V ETTERL IM. Adaptive wavelet threshold for image de-noising compression [J]. IEEE Trans. Image Processing, Vol. 9, 2000:1532-1546.
[53]郭晓霞,杨慧中.小波去噪中软硬阈值的一种改良折衷法[J].智能系统学报,Vol.3,NO.3,2008:222-225.
[54]王振国,汪恩华.小波包相关阀值去噪[J].石油物探,Vol.41(4),2002:400-405.
[55] DONG Yongsheng, YI Xuming. Wavelet de-noising based on four improved functions for threshold estimation [J]. Journal of Math, Vol.26 (5), 2006: 473-477.
[56]孙蕾,谷德峰,罗建书.基于迭代方法的软阈值估计小波去噪[J].系统工程与电子技术,Vol.31,No.1,2009:36-39.
[57]邓禹,熊静琪,范显峰.基于小波变换的混合阈值去噪的方法研究[J].光通信研究,No.3,2008:67-69.
[58] Hong H, Liang M. De-noising mechanical signals by hybrid thresholding [C]. Robotic Sensors Robotic and sensor Environment s Ottawa, Ontario, Canada: IEEE, 2005: 65-70.
[59] Johnstone I M, Silverman B-W. Wavelet threshold estimators for data with correlated noise[J]. Journal of royal statistics society series(B), 1997, 59:319～351.
[60]赵瑞珍,屈汉章,宋国乡.基于小波系数区域相关性的阈值滤波算法[J].西安电子科技大学学报(自然科学版),Vol.28,No.3,2001:324-327.
[61] Johnstone I M, Silverman B W. Wavelet threshold estimators for data with correlated noise [J]. Journal of the Royal Statistical Society: Series B, Vol.59 (2), 1997:319-351.
[62]尚晓清,王军锋,宋国乡.基于Bayesian估计和Wiener滤波的阈值去噪方法[J].光子学报,Vol.32 (7),2003:889-891.
[63] Chang S G, Yu B in and M art inv1 Adaptive wavelet thresholding for image deno ising and compression1 [J]. IEEE Trans On Image Processing, 2000( 9): 1532-1546.
[64] HOU Jianhua , TIAN Jinwen ,LIU Jian. Analysis of the errors in locally adaptive wavelet domain wiener filter and image denoising[J]. Acta Photonica S inica, Vol.36 (1), 2007: 188-191.
[65]曾守桢,穆志民.基于小波阈值去噪方法的一种改进方案[J].天津农学院学报,Vol.15,No.1,2008:4-7.
[66]崔华,宋国乡.基于小波阈值去噪方法的一种改进方案[J].现代电子技术,Vol.28 (1),2005:8-9.
[67]付炜,许山川.一种改进的小波域阈值去噪算法[J].传感技术学报,Vol.19 (2),2006:534-540.
[68]周怀来.基于小波变换的地震信号去噪方法研究与应用[D].成都理工大学硕士学位论文,2006.
[69]满蔚仕,高静怀.垂直地震剖面资料中的随机噪声衰减[J].西安交通大学学报,Vol.40,No.12,2006:1419-1423.
[70]张旭莲.小波变换及其在地震资料去噪中的应用[D].西安电子科技大学硕士论文,2006.
[71]姚胜利.地震信号的小波去噪方法研究[D].中南大学硕士论文,2007.
[72]赵晨,赵瑞珍,甘小冰.小波分析·应用算法.北京:科学出版社,2004
[73]牟泽霖,李才明,杨伟刚.基于小波变换尺度相关性去噪算法的改进[J].内蒙古石油化工,No.11,2006:147-149
[74]陈东义,曹长修,朱冰莲,周建伟.一种简化的小波去噪算法[J].重庆大学学报,Vol.20(5),1997:673-681.
[75]熊先泽,李言俊,张科,祁飞.基于模糊理论的空间屏蔽滤波信号去噪[J].光子学报,Vol.37,No.10,2008:2099-2102.
[76]吴冬梅.基于平移不变小波阈值算法的噪音图象估计[J].光子学报,Vol.34(2),2005:306-309.
[77]毛伟,林春生,吴正国.一种基于SSNF的新型阈值滤波去噪算法[J].海军工程大学学报,Vol.19,No.6,2007:75-78.
[78]李晋平,王大庆,许新刚.用MATLAB实现地震数据的小波变换[J].物探化探计算技术,Vol.124,No.2,2002:163-168.
[2].陆基孟.地震勘探原理.北京:石油大学出版社,1993.
[3]张德忠.陆上石油地震勘探技术进步50年[J].石油地球物理勘探,Vol.35.No.5,2000:545-558.
[4]杨建广,吕绍林.地球物理信号处理技术的研究及进展[J].地球物理学进展,Vol.17,No.1,2002:171-175.
[5]付燕.人工地震信号去噪方法研究[D].西安:西北工业大学出版社,2002.
[6]张军华,吕宁,田连玉,陆文志,钟磊.地震资料去噪方法技术综合评述[J].地球物理学进展,Vol.21,No.2,2006:546-553.
[7]李鸣社.地震勘探资料数字处理[M].中国矿业大学出版社,1989.
[8]文莉,刘正士,葛运建.小波去噪的几种方法[J].合肥工业大学学报(自然科学版),2002,25(2):167-172。
[9]蒋录全,何光明.小波理论及其在地震勘探中的应用[J].地质科技情报,Vol.14 (1),1995,892-893.
[10]赵玉宝.小波变换在地震信号去噪中的应用研究[D].中南大学硕士论文,2005.
[11]黄力军.浅谈地震信号中的噪声及去除方法[J].内蒙古石油化工,No.4,2008,31-34.
[12]梁学章,何甲兴,王新民,李强.小波分析[M].北京:国防工业出版社,2005.
[13]程正兴.小波分析算法与应用[M].西安:西安交通大学出版社,1998.
[14]裴正林.小波理论及其在地震数据处理中的应用[J].地球物理学进展,Vol.17,No.3,2002:486-490.
[15]高静怀,汪文秉,朱光明等.地震资料处理中小波函数的选取研究[J].地球物理学报,39(3),1996:392～400.
[16]秦前清,杨宗凯.实用小波分析[M].西安:西安电子科技大学出版社,1998.
[17]刘春生,张晓春.实用小波分析[M].徐州:中国矿业大学出版社,2002.
[18]岑翼刚,岑丽辉,孙德宝.信号Lipschitz奇异性的计算与分析[J].计算机工程与应用,Vol.18,2004,35-37.
[19]覃太贵,张学英,羿旭明.小波变换在信号奇异性检测中的应用[J].数学杂志,24(3),2004:323-326.
[20]张小飞,徐大专,齐泽锋.基于小波变换奇异信号检测的研究[J].系统工程与电子技术,2003,25(7):814-816.
[21]戴建新,郦志新,宋洪雪.基于小波的信号Lipschitz指数分析和应用[J].南京邮电大学学报(自然科学版),Vol.28,No.6,2008:69-73.
[22] Cvetkovic Z. Vetterli M. Discrete-time wavelet extreme representation: Design and consistent reconstruction [J]. IEEE Trans Signal Processing.1995, 43(3): 681-693.
[23] Liu G Z, Zhang Z M. Iterative shaping reconstruction algorithm based on the modules maxima of signal’s dyadic wavelet transform [J]. Progress in Natural Science, 2000, 10(8): 660-664.
[24] Mallat S, Zhang S. Characterization of signal from multi-scale edges[J]. IEEE Trans Pattern Analysis and Machine Intelligence, 1992, 14(7): 710-732.
[25] J.Morlet, G.Arens, E.Fourgeau and D.Giard. Wave propagation and sampling theory-part I: Complex signal and scattering multilayered media [J].Geophysi cs, 47(2), 1982:203-221.
[26] Mallat S. Zero-crossings of a wavelet transform. IEEE Trans Information Theory [J]. 37(4), 1991:1019-1033.
[27]陈德智,唐磊.由小波变换的模极大值快速重构信号[J].电子学报,26(9),1998: 82-85.
[28]廖国勇,徐长友.一种快速重构信号的方法[J].华中科技大学学报,30(8),2002:98-100.
[29]蔡汉添,宋勇.关于子波变换局部极大值信号重构的交替投影算法[J].数据采集与处理,1998,Vol.13(2):112-116.
[30]张茁生,刘贵忠,刘峰.一种新的信号二进小波变换模极大值重构信号的迭代算法[J].中国科学,Vol.33,No.6,2003:545-553.
[31]何永红,文鸿雁,靳鹏伟.一种基于小波模极大值去噪的改进算法[J].大地测量与地球动力学,Vol.27,No.2,2007:94-98.
[32]韩民,田岚.基于Hermite插值的小波变换模极大值重构信号快速算法[J].系统仿真学报,Vol.11,No.2,12005:626-2 619.
[33]张兆宁,董肖红,潘云峰.基于小波变换模极大值去噪方法的改进[J].电力系统及其自动化学报.Vol.17,No.2,2005:9-12.
[34] Hsung Taichiu, Lun Daniel Pakkong, Siu Wanchi. Denoising by singularity detect ion [J]. IEEE T ranson Signal Processing, 1999, 47 (11): 3139-3144.
[35]王和平,康景利.一种基于小波模极大值的信号去噪算法[J].系统工程与电子技术,Vol.27,No.11,2005:1876-1877.
[36]张军萍,蔡汉添.基于子波变换局部极大值的信号去噪新算法[J].电路与系统学报,Vol.2(2),1997:31-34.
[37]顾意农,张志宏,吴正国,郑学铃.基于小波变换模极大值恢复的信号消噪方法[J]海军工理大学学报,13(2):25-32,2001
[37] David L. Donoho. De-Noising by Soft-Thresholding [J]. IEEE TRANS. ON INFORMATION THEORY, VOL. 41, NO. 3, 1995:613-627.
[38]袁兰敬.小波变换在信号去噪中的应用[D].中国地质大学(北京),硕士论文,2008.
[39] BAKHTAZAD A, PALAZOGLU A, ROMANGOL I J A. Process data denoising usingwavelet transform[J]. Telligent Data Analysis, Vol.3 (4), 1999: 267-285.
[40] XU Yansun. Wavelet transform domain filters: a spatially selective noise filtration technique [J]. IEEE Trans on Image Processing, Vol.3 (6), 1994 : 747 - 758.
[41]夏洪瑞,朱勇,周开明.小波变换及其在去噪中的应用[J].石油地球物理勘探,Vol.29 (3),1994:274～285.
[42]刘庆普,胡留军.地震数据去噪中的小波方法[J].哈尔滨工程大学学报,Vol.23,NO.4,2002:86-90.
[43] ZhangLei, Pan Quan, et al. On the determination of threshold in threshold based denoising by wavelet transformation [J]. Acta Electronic a Sinica, Vol.29 (3) , 2001: 400-403.
[44] Azzalini A , Farge M , Schneider K. Nonlinear wavelet thresholding: A recursive method to determine the optimal denoising threshold [J]. Appl. Comput. Harmon. A nal, 2005 (18):177- 185.
[45]李华.小波理论分析及其在地震信号处理中的应用研究[D].成都:成都理工学院,2000.
[46]张媛玲.小波分析在地震勘探资料处理中的应用[D].沈阳:沈阳工业大学,2001.
[47]张吉先,钟秋海,戴亚平.小波门限消噪法应用中分解层数及阈值的确定[J].中国电机工程学报,Vol24,No.2,2004:118-122.
[48]潘泉,戴冠中,张洪才.具有理论阈值的小波滤波方法[J].宇航学报,Vol.19(4),1998:81-85.
[49]刘永峰,武俊,王晓光.一种基于小波阈值去噪的改进方法[J].电脑知识与技术,2006:154-155.
[50]陶红艳,秦华峰,余成波.基于改进阈值函数的小波域去噪算法的研究[J].压电与声光,Vol.30,No.1,2008:93-95.
[51]侯锐锋.小波变换在地震资料随机噪声去除中的应用[D].成都理工大学硕士论文,2009.
[52] CHAN G S, YU B, V ETTERL IM. Adaptive wavelet threshold for image de-noising compression [J]. IEEE Trans. Image Processing, Vol. 9, 2000:1532-1546.
[53]郭晓霞,杨慧中.小波去噪中软硬阈值的一种改良折衷法[J].智能系统学报,Vol.3,NO.3,2008:222-225.
[54]王振国,汪恩华.小波包相关阀值去噪[J].石油物探,Vol.41(4),2002:400-405.
[55] DONG Yongsheng, YI Xuming. Wavelet de-noising based on four improved functions for threshold estimation [J]. Journal of Math, Vol.26 (5), 2006: 473-477.
[56]孙蕾,谷德峰,罗建书.基于迭代方法的软阈值估计小波去噪[J].系统工程与电子技术,Vol.31,No.1,2009:36-39.
[57]邓禹,熊静琪,范显峰.基于小波变换的混合阈值去噪的方法研究[J].光通信研究,No.3,2008:67-69.
[58] Hong H, Liang M. De-noising mechanical signals by hybrid thresholding [C]. Robotic Sensors Robotic and sensor Environment s Ottawa, Ontario, Canada: IEEE, 2005: 65-70.
[59] Johnstone I M, Silverman B-W. Wavelet threshold estimators for data with correlated noise[J]. Journal of royal statistics society series(B), 1997, 59:319～351.
[60]赵瑞珍,屈汉章,宋国乡.基于小波系数区域相关性的阈值滤波算法[J].西安电子科技大学学报(自然科学版),Vol.28,No.3,2001:324-327.
[61] Johnstone I M, Silverman B W. Wavelet threshold estimators for data with correlated noise [J]. Journal of the Royal Statistical Society: Series B, Vol.59 (2), 1997:319-351.
[62]尚晓清,王军锋,宋国乡.基于Bayesian估计和Wiener滤波的阈值去噪方法[J].光子学报,Vol.32 (7),2003:889-891.
[63] Chang S G, Yu B in and M art inv1 Adaptive wavelet thresholding for image deno ising and compression1 [J]. IEEE Trans On Image Processing, 2000( 9): 1532-1546.
[64] HOU Jianhua , TIAN Jinwen ,LIU Jian. Analysis of the errors in locally adaptive wavelet domain wiener filter and image denoising[J]. Acta Photonica S inica, Vol.36 (1), 2007: 188-191.
[65]曾守桢,穆志民.基于小波阈值去噪方法的一种改进方案[J].天津农学院学报,Vol.15,No.1,2008:4-7.
[66]崔华,宋国乡.基于小波阈值去噪方法的一种改进方案[J].现代电子技术,Vol.28 (1),2005:8-9.
[67]付炜,许山川.一种改进的小波域阈值去噪算法[J].传感技术学报,Vol.19 (2),2006:534-540.
[68]周怀来.基于小波变换的地震信号去噪方法研究与应用[D].成都理工大学硕士学位论文,2006.
[69]满蔚仕,高静怀.垂直地震剖面资料中的随机噪声衰减[J].西安交通大学学报,Vol.40,No.12,2006:1419-1423.
[70]张旭莲.小波变换及其在地震资料去噪中的应用[D].西安电子科技大学硕士论文,2006.
[71]姚胜利.地震信号的小波去噪方法研究[D].中南大学硕士论文,2007.
[72]赵晨,赵瑞珍,甘小冰.小波分析·应用算法.北京:科学出版社,2004
[73]牟泽霖,李才明,杨伟刚.基于小波变换尺度相关性去噪算法的改进[J].内蒙古石油化工,No.11,2006:147-149
[74]陈东义,曹长修,朱冰莲,周建伟.一种简化的小波去噪算法[J].重庆大学学报,Vol.20(5),1997:673-681.
[75]熊先泽,李言俊,张科,祁飞.基于模糊理论的空间屏蔽滤波信号去噪[J].光子学报,Vol.37,No.10,2008:2099-2102.
[76]吴冬梅.基于平移不变小波阈值算法的噪音图象估计[J].光子学报,Vol.34(2),2005:306-309.
[77]毛伟,林春生,吴正国.一种基于SSNF的新型阈值滤波去噪算法[J].海军工程大学学报,Vol.19,No.6,2007:75-78.
[78]李晋平,王大庆,许新刚.用MATLAB实现地震数据的小波变换[J].物探化探计算技术,Vol.124,No.2,2002:163-168.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |