基于第二代小波变换的测井信号处理

小波分析技术近几年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，有大量的卷积运算，运算速度较慢，硬件实现复杂，内存占用大。文章提出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。并将结果和传统小波变换的结果进行了对比，得到了优于传统小波变换的效果。第二代小波变换运算速度快，硬件实现容易，内存占用少，在测井信号去噪处理方面有着广阔的应用前景。

Logging signal processing based on the second generation wavelet transform

Traditional wavelet transform depends on Fourier transform and has many convolution operation,these make its operation speed slow,achievement camplicated and memory occupancy more. The second generation wavelet transform based on the lifting scheme in denoising logging signal processing is proposed. Lifting scheme is honored as the key tool to the construction of the second generation wavelets. Through analyzing the base principle of lifting scheme,it is fetched out that it decompose the logging signal at the different distinguish rates,and process the detail coefficient of wavelet transform by soft function of limiting range. The processed detail coefficient and the relevant coefficient are used to construct the logging signal. Contrasted with the traditional wavelet transform,the second generation wavelet transform has more excelled result,with fast operation speed,flexible hardware and a few memory,these make it has wide foreground in denoising logging signal processing.