基于提升算法的测井信号去噪处理

近几年，小波分析技术在测井信号去噪处理方面得到了较为广泛的应用，但是传统的小波变换依赖于傅立叶变换，因而有大量的褶积运算，占用内存大，运算速度较慢。为此，采用基于提升算法的第二代小波变换来进行测井信号的去噪处理，提升算法是构造第二代小波的关键技术。通过分析提升算法的基本原理，尝试使用第二代小波对测井信号进行不同分辨率下的分解处理，并使用软限幅函数处理小波分解的细节系数，将处理过的细节系数和近似系数一起重构信号。第二代小波变换的结果与传统小波变换的结果对比表明第二代小波变换的处理效果要优于传统的小波变换，而且运算速度快，占用内存小。

Denoising of logging data using lifting scheme

The traditional wavelet transform depends on Fourier transform and involves a lot of convolutional operation, which in turn makes the operation speed slow and consumes a large amount of memory. We developed a method to remove the noises in well log- ging data by the second-generation wavelet transfor- mation. The key to construct the second-generation wavelet is the lifting scheme. The well logging data are firstly decomposed under different resolutions. Detailed coefficients of wavelet transform are deter- mined by using soft thresholding function. The de- tailed coefficients and the relevant coefficients are then used to reconstruct the well logging data. Com- parisons show that the new method yields superior results.