第二代小波变换及其在地震信号去噪中的应用(英文)
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摘要
本文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,基于提升法的小波变换是一种柔性的小波构造方法,它使用线性、非线性或空间变化的预测和更新算子,并能确保变换的可逆性。通过对模拟数据和实际资料的处理,证明了的它对地震信号去噪具有很好的效果。离散信号的小波去噪可分为三步:小波分解,系数缩减(切除噪声部分),信号重建。目前常用的小波去噪的方法有硬阈值法和软阈值法,这里采用软阈值法去噪。本文的提升变换采用的是Deslauriers-Dubuc(4,2)小波,基于以上变换方法,分别对含噪的模拟数据及实际地震数据进行3级可逆提升变换,对每一级上的细节信号按上述的软域值法进行处理,削减小波系数中的噪声部分,从而实现了信号去噪,结果证明去除随机噪声的效果是令人满意的。
This paper discusses the principle and procedures of the second-generation wavelet trans- form and its application to the denoising of seismic data. Based on lifting steps, it is a flexible wavelet construction method using linear and nonlinear spatial prediction and operators to implement the wavelet transform and to make it reversible. The lifting scheme transform includes three steps: split, predict, and update. Deslauriers-Dubuc (4, 2) wavelet transforms are used to process both synthetic and real data in our second-generation wavelet transform. The processing results show that random noise is effectively suppressed and the signal to noise ratio improves remarkably. The lifting wavelet transform is an efficient algorithm.
This paper discusses the principle and procedures of the second-generation wavelet trans- form and its application to the denoising of seismic data. Based on lifting steps, it is a flexible wavelet construction method using linear and nonlinear spatial prediction and operators to implement the wavelet transform and to make it reversible. The lifting scheme transform includes three steps: split, predict, and update. Deslauriers-Dubuc (4, 2) wavelet transforms are used to process both synthetic and real data in our second-generation wavelet transform. The processing results show that random noise is effectively suppressed and the signal to noise ratio improves remarkably. The lifting wavelet transform is an efficient algorithm.
引文
Daubechies, Sweldens W., 1994, Factoring wavelet trans-form into lifting steps: J. Fourier Anal. Appl. 4 (3).
Donoho D. L., 1995, Denoising by soft-thresholding: IEEETrans. Inf. Theory, 41, 613-627.
Feng Lin et al, 2004, Denoising of logging data using lift-ing Scheme: Geophysical Prospecting for Petroleum,43(3): 238-241.
Li Qingzhong, 1994, A way to the precise exploration:China Petroleum industry press.
Sweldens W, 1997, Lossless image compression usinginteger to integer wavelet transforms: International con-ference on image processing, 1(1), 5966599.
Sweldens W, 1998, The lifting scheme: A construction ofsecond generation wavelets: SIAM J. Math. Anal., 29,511-546.
Tang Yan et al, 2000, Application of second-generationwavelet transform to the lossless image compressioncoding: Chinese Journal of Image and Graphics, 8.
Wang Zhiwu et al, 2002, Adaptive lifting wavelet trans-forms and denoising: Computer engineering andapplications, 2.
Zhang Xueying et al, 2004, Signal Denoising with Nonlin-ear lifting Scheme: J. of Math. (Chinese), 24(2), 193-196.
Donoho D. L., 1995, Denoising by soft-thresholding: IEEETrans. Inf. Theory, 41, 613-627.
Feng Lin et al, 2004, Denoising of logging data using lift-ing Scheme: Geophysical Prospecting for Petroleum,43(3): 238-241.
Li Qingzhong, 1994, A way to the precise exploration:China Petroleum industry press.
Sweldens W, 1997, Lossless image compression usinginteger to integer wavelet transforms: International con-ference on image processing, 1(1), 5966599.
Sweldens W, 1998, The lifting scheme: A construction ofsecond generation wavelets: SIAM J. Math. Anal., 29,511-546.
Tang Yan et al, 2000, Application of second-generationwavelet transform to the lossless image compressioncoding: Chinese Journal of Image and Graphics, 8.
Wang Zhiwu et al, 2002, Adaptive lifting wavelet trans-forms and denoising: Computer engineering andapplications, 2.
Zhang Xueying et al, 2004, Signal Denoising with Nonlin-ear lifting Scheme: J. of Math. (Chinese), 24(2), 193-196.
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