平稳小波变换在探地雷达资料降噪中的应用
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摘要
小波变换方法是一种新的数学方法,具有强大的时频分析能力,广泛地应用到信号处理的各个领域。其中正交小波变换不具备线性相位、不具有平移不变性等特性,导致其在信号降噪领域仍存在很多问题,会使信号产生振荡现象。本文利用平稳小波变换对多组探地雷达模型实验与实际雷达资料的处理,说明该方法较好地保留了信号边缘细节,避免了伪Gibbs现象,其降噪效果明显优于普通正交小波方法的降噪效果。
The wavelet transform is a new mathematical method which has a strong ability to analyse time-frequency.It's widely applied to various fields of signal processing.Orthogonal wavelet transform is not possessed with linear phase or translation invariant features,so there are still many problems in the field of signal noise reduction,such as signal oscillation phenomenon.In this paper,we applied stationary wavelet transform to some ground penetrating radar models and the filed radar data.The results show that this method retains the edge of the signal details and avoids the phenomenon of pseudo-Gibbs.Noise reduction effect of stationary wavelet transform is superior to ordinary orthogonal wavelet method.
The wavelet transform is a new mathematical method which has a strong ability to analyse time-frequency.It's widely applied to various fields of signal processing.Orthogonal wavelet transform is not possessed with linear phase or translation invariant features,so there are still many problems in the field of signal noise reduction,such as signal oscillation phenomenon.In this paper,we applied stationary wavelet transform to some ground penetrating radar models and the filed radar data.The results show that this method retains the edge of the signal details and avoids the phenomenon of pseudo-Gibbs.Noise reduction effect of stationary wavelet transform is superior to ordinary orthogonal wavelet method.
引文
[1]李大心.探地雷达方法与应用[M].北京:地质出版社,1994.
[2]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,2002,17(3):486~490.
[3]刘天佑.位场勘探数据处理新方法[M].北京.科学出版社,2007.
[4]候遵泽,杨文采.中国重力异常的小波变换与多尺度分析[J].地球物理学报,1997,40(1):85~95.
[5]杨文采,施志群,侯遵泽,等.离散小波变换与重力异常多重分解[J].地球物理学报,2001,44(4):534~541.
[6]耿喜哲,刘天佑.小波分析在高精度磁测数据处理上的应用[J].石油物探,2000,39(4):121~124.
[7]钟凌云.小波变换方法在地震资料噪声消除中的应用[J].物探与化探,2007,31(3):245~249.
[8]刘宏,何兰芳,王绪本,等.小波分析在MT去噪处理中的适定性[J].石油地球物理探,2004,39(3):338~341.
[9]David L Donoho.Denoising by soft thresholding[J].IEEE Transactions on Information Theory,1995,41(3):613~627.
[10]G P Nason,B W Silverman.The stationary wavelettransform and some statistical applications in wave-let and statistics.In:A Antoniadis ed.LectureNotes in Statistics[C].Berlin:Spinger Verlag,1995.281~299.
[11]高清维,李斌,解光军,等.基于平稳小波变换的图像去噪方法[J].计算机研究与发展,2002,39(12):1689~1694.
[12]赵艳粉,杨洪耕.二维离散小波变换在电能质量检测数据压缩中的应用[J].电力系统自动化,2006,30(15):51~55.
[13]李霖,杨洪耕.基于二维离散平稳小波变换的短时电能质量扰动检测方法[J].电力系统自动化,2007,31(10):21~25.
[14]李淑霞,王汝霖,许亮,等.双正交冗余小波变换的图像去噪方法[J].光电工程,2007,34(3):89~92,144.
[15]陈玉东.地球物理信息处理基础[M],北京:地质出版社,2006.
[16]朱希安,金声震,宁书年,等.小波分析的应用现状及展望[J].煤田地质与勘探,2003,31(2):51~55.
[17]黄南晖.地质雷达探测的波场分析[J].地球科学-中国地质大学学报,1993,18(3):294~302.
[18]邓世坤.探地雷达图象的正演合成[J].地球科学-中国地质大学学报,1993,18(3):285~293.
[2]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,2002,17(3):486~490.
[3]刘天佑.位场勘探数据处理新方法[M].北京.科学出版社,2007.
[4]候遵泽,杨文采.中国重力异常的小波变换与多尺度分析[J].地球物理学报,1997,40(1):85~95.
[5]杨文采,施志群,侯遵泽,等.离散小波变换与重力异常多重分解[J].地球物理学报,2001,44(4):534~541.
[6]耿喜哲,刘天佑.小波分析在高精度磁测数据处理上的应用[J].石油物探,2000,39(4):121~124.
[7]钟凌云.小波变换方法在地震资料噪声消除中的应用[J].物探与化探,2007,31(3):245~249.
[8]刘宏,何兰芳,王绪本,等.小波分析在MT去噪处理中的适定性[J].石油地球物理探,2004,39(3):338~341.
[9]David L Donoho.Denoising by soft thresholding[J].IEEE Transactions on Information Theory,1995,41(3):613~627.
[10]G P Nason,B W Silverman.The stationary wavelettransform and some statistical applications in wave-let and statistics.In:A Antoniadis ed.LectureNotes in Statistics[C].Berlin:Spinger Verlag,1995.281~299.
[11]高清维,李斌,解光军,等.基于平稳小波变换的图像去噪方法[J].计算机研究与发展,2002,39(12):1689~1694.
[12]赵艳粉,杨洪耕.二维离散小波变换在电能质量检测数据压缩中的应用[J].电力系统自动化,2006,30(15):51~55.
[13]李霖,杨洪耕.基于二维离散平稳小波变换的短时电能质量扰动检测方法[J].电力系统自动化,2007,31(10):21~25.
[14]李淑霞,王汝霖,许亮,等.双正交冗余小波变换的图像去噪方法[J].光电工程,2007,34(3):89~92,144.
[15]陈玉东.地球物理信息处理基础[M],北京:地质出版社,2006.
[16]朱希安,金声震,宁书年,等.小波分析的应用现状及展望[J].煤田地质与勘探,2003,31(2):51~55.
[17]黄南晖.地质雷达探测的波场分析[J].地球科学-中国地质大学学报,1993,18(3):294~302.
[18]邓世坤.探地雷达图象的正演合成[J].地球科学-中国地质大学学报,1993,18(3):285~293.
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