第二代小波变换及其在地震信号去噪中的应用
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摘要
第二代小波变换是从传统小波理论发展起来的一个分支,与第一代小波变换相比它有如下特点:①继承了第一代小波的多分辨率特性;②不依赖于傅里叶变换;③易实现快速算法;④逆变换易实现;⑤可实现非线性小波变换等。目前对第二代小波的研究还处于起步阶段,其应用主要是在图像处理领域。讨论了第二代小波变换的基本原理和变换过程,并将第二代小波变换引入到地震资料去噪处理中,通过对模拟数据和实际资料的处理,证明了它对地震信号去噪具有很好的效果。
Second-generation wavelet transform is a branch derived from traditional wavelet theory. Compared with the first-generation wavelet transform, its features include: ①keep the multi-resolution feature of first-generation wavelet. ②Independent of Fourier Transform ③Fast a rithmetic is easily to be achieved.④Reverse transform is easier.⑤Non-linear wavelet transform is available, etc. At presently, the research for second-generation wavelet transform is on the earlier stage and its application is mainly limited to image processing field The principle and procedures of second-generation wavelet transform and application in the de-noising of seismic data are discussed in the paper. Examples on synthetic as well as field data prove that it is a new effective squelch method.
Second-generation wavelet transform is a branch derived from traditional wavelet theory. Compared with the first-generation wavelet transform, its features include: ①keep the multi-resolution feature of first-generation wavelet. ②Independent of Fourier Transform ③Fast a rithmetic is easily to be achieved.④Reverse transform is easier.⑤Non-linear wavelet transform is available, etc. At presently, the research for second-generation wavelet transform is on the earlier stage and its application is mainly limited to image processing field The principle and procedures of second-generation wavelet transform and application in the de-noising of seismic data are discussed in the paper. Examples on synthetic as well as field data prove that it is a new effective squelch method.
引文
1 郭刚明,时立彩,高生军,等.小波变换在地震资料处理 中的应用效果分析[J].石油物探,2003,42(2):237- 239
2 刘培题,刘喜武,年静波.用过采样小波变换提高地震资 料分辨率[J].石油物探,2003,42(4):513-516
3 王西文,苏明军,刘军迎,等.基于小波变换的地震相干 体算法及其应用[J].石油物探,2002,41(3):334-338
4 Daubechies I, Sweldens W. Factoring wavelet transform into lifting steps [J]. Journal of Fourier Analysis Application, 1994,4(3) :247-269
5 王志武,丁国清,颜国正,等.自适应提升小波变换与信 号去噪[J].计算机工程与应用,2002(2):28-30
6 Sweldens W. Lossless image compression using integer to integer wavelet transforms[J]. International conference on image processing, 1997,1(1) :596-599
7 Antonini M, Barlaud, Mathieu Petal. Image coding u sing the wavelet transform [J]. IEEE Transaction on image Processing, 1992,1(2) :205-220
8 汤焱,莫玉龙.二代小波变换应用于图象的无损压缩编 码[J].中国图像图形学报,2000,5(A版):699-702
9 Donoho D L. Denoising by soft-thresholding [J]. IEEE Transactions on Information Theory, 1995, 41 (3): 613-627
10 阚伟,张郑擎,朱秋煜.二代小波在MPEG-4任意形状 图象变换编码中的应用[J].电路与系统学报,2001,6 (1):88-92
2 刘培题,刘喜武,年静波.用过采样小波变换提高地震资 料分辨率[J].石油物探,2003,42(4):513-516
3 王西文,苏明军,刘军迎,等.基于小波变换的地震相干 体算法及其应用[J].石油物探,2002,41(3):334-338
4 Daubechies I, Sweldens W. Factoring wavelet transform into lifting steps [J]. Journal of Fourier Analysis Application, 1994,4(3) :247-269
5 王志武,丁国清,颜国正,等.自适应提升小波变换与信 号去噪[J].计算机工程与应用,2002(2):28-30
6 Sweldens W. Lossless image compression using integer to integer wavelet transforms[J]. International conference on image processing, 1997,1(1) :596-599
7 Antonini M, Barlaud, Mathieu Petal. Image coding u sing the wavelet transform [J]. IEEE Transaction on image Processing, 1992,1(2) :205-220
8 汤焱,莫玉龙.二代小波变换应用于图象的无损压缩编 码[J].中国图像图形学报,2000,5(A版):699-702
9 Donoho D L. Denoising by soft-thresholding [J]. IEEE Transactions on Information Theory, 1995, 41 (3): 613-627
10 阚伟,张郑擎,朱秋煜.二代小波在MPEG-4任意形状 图象变换编码中的应用[J].电路与系统学报,2001,6 (1):88-92
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