第二代小波变换及其在地震信号去噪中的应用

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。

The second-generation wavelet transform and its application in denoising of seismic data

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.