利用平衡双正交多小波变换进行地震数据去噪与压缩
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摘要
本文通过实例讨论了利用平衡双正交多小波变换对地震数据进行去噪处理和数据压缩的过程。去噪过程为 :1在多小波变换域上 ,利用高频高波数分量来估计随机噪声的方差 ;2利用地震记录的方差减去噪声的方差得到有效信号的方差 ,从而求出阈值 ,并采用软阈值处理方法进行去噪 ;3利用多小波反变换公式得到去噪后的信号。数据压缩过程为 :1利用平衡双正交多小波 BSA6 /6把地震数据分解成 4层 ,每次只对低频部分进行分解 ;2重排每个 2× 2子块 ,使得具有相同空间位置关系的 4个系数排在一起 (原来的 1 6个子块变为 4个子块 ) ,从而满足 SHIFT编码方案中所要求的父子关系 ;3对每个等级树进行嵌入式编码 ,利用改进的小波零树编码方案压缩地震数据。试验结果表明 ,文中方法优于单小波去噪与数据压缩方法。
Through the real cases,the paper discussed t- he process using balanced biorthogonal multi-wavelets transform to implement noise-elimination and data compression of seismic data.The processes of noise-elimination are follows:①using components of high-frequency and high-wavenumber to evaluate variance of random noise in multi-wavelets domain;②variation of seismic data minus variance of noise is equal to variance of useful signal,then threshold is computed,using soft threshold value processing method for noise-elimination;③the noise-eliminated signals are resulted from the inversion wavelet transform.The processes of data compression are follows:①decomposing the seismic data into 4 layers by balanced biorthogonal wavelets BSA6/6,the decomposition is carried out only for low-frequency parts each time;②rearranging each 2×2 sub-block so that the 4 coefficients that have same special positions are arranged together(original 16 sub-blocks now became 4 sub-blocks),that met the parent-child relationship required by SHIFT coding scheme;③embedded coding is carried out for the tree of each level,using improved wavelet zero-tree code scheme to compress seismic data.Experiment results showed that the method in the paper is superior to the noise-elimination and data compression methods by single wavelet.
Through the real cases,the paper discussed t- he process using balanced biorthogonal multi-wavelets transform to implement noise-elimination and data compression of seismic data.The processes of noise-elimination are follows:①using components of high-frequency and high-wavenumber to evaluate variance of random noise in multi-wavelets domain;②variation of seismic data minus variance of noise is equal to variance of useful signal,then threshold is computed,using soft threshold value processing method for noise-elimination;③the noise-eliminated signals are resulted from the inversion wavelet transform.The processes of data compression are follows:①decomposing the seismic data into 4 layers by balanced biorthogonal wavelets BSA6/6,the decomposition is carried out only for low-frequency parts each time;②rearranging each 2×2 sub-block so that the 4 coefficients that have same special positions are arranged together(original 16 sub-blocks now became 4 sub-blocks),that met the parent-child relationship required by SHIFT coding scheme;③embedded coding is carried out for the tree of each level,using improved wavelet zero-tree code scheme to compress seismic data.Experiment results showed that the method in the paper is superior to the noise-elimination and data compression methods by single wavelet.
引文
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[2] JiaR Q et al.Vector subdivision schemes andmultiple wavelets.Math omp,1998,67:1533～1563
[3] StrangG et al.Orthogonal multiwavelets withvanishing m om ents.J OpticalEng,1994,33:2104～2107
[4] StrangG et al.Short wavelets and matrix dilationequations.IEEE TransSP,1995,43:108～115
[5] L ebrunJ et al.High- order balanced m ultiwavelets:theory,factorization and design.IEEE TransSP,2001,49(9):1918～1929
[6] QingtangJ.Orthogonal multiwavelets with optimumtim e- frequency resolution.IEEE TransSP,1998,46:830～844
[7] HweeH T et al.New biorthogonal m ultiwavelets forim age com pression.SignalProsessing,1999,79:45～65
[8] JamesE F et al.Wavelet transform s for vector fieldsusing om nidirectionally balanced m ultiwavelets.IEEE TransSP,2002,50(12):3018～3027
[9] ChangS G et al.Adaptive wavelet thresholding forimage denoising and com pression.IEEE TransIP,2000,1532～1546
[10] ShaprioJM.Em edded im age coding using zerotreesof wavelet coefficients.IEEE TransSP,1993,41(12):3445～3462
[11] 吴爱弟,牟永光.地震数据的小波包压缩方法.石油大学学报,1996,20(6):5～8
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