基于小波变换的高密度电法资料去噪研究

Research on High-density Electrical Data Denoising Based on Wavelet Transform Method

小波变换方法是近年来发展起来的一种新的数学方法,目前,小波分析已经成为国际上公认的最新时频分析工具,成为多学科共同关注的焦点,尤其是它可以对离散性信号进行非线性降噪处理。传统的高密度电阻率信号降噪处理一般采用坏点切除、滑动平均或偏值滤波的方法,即采用线性方法经行降噪,不能很有效地突出有用异常信号、完全去除畸变点,从而不能为后期处理提供可靠的电阻率数据。小波降噪成功主要得益于小波变换有低熵性、多分辨率特性、去相关性和选基灵活性等特点。它的原则是要尽量保持原始信号的光滑性和相似性。小波分析的实质是对原始信号进行分解,然后通过特定的阈值进行滤波,最后对降噪后的信号进行重建。因此很好地保持了有用的异常信号,提高了信噪比。

Wavelet transform method is a new mathematical method which has been developed in recent years.Nowadays,wavelet analysis is internationally recognized as the newest time-frequency analysis tool,and becomes the concern focus of many academic subjects.Traditional signal denoising methods of high-density resistivity are generally used such as removing dead pixels,moving average,and partial value filtering,etc.,that is,using the linear methods to reduce the noise cannot effectively highlight the useful abnormal signals and not completely remove the distortion points,thus,the methods cannot provide reliable resistivity data for post-processing.However,the wavelet analysis uses nonlinear methods of noise reduction to process discrete signals.The success of wavelet denoising method is mainly due to the features of wavelet transform,such as low entropy,multi-resolution,decorrelation,and flexibility of base selection,etc.The principle of the wavelet analysis is to keep the smoothness and the similarity of the original signals.And its essence is to decompose the original signals,and then filter the waves by means of fixed threshold,and finally reconstruct the denoised signals.Therefore,the useful abnormal signals are well maintained and the signal to noise ratio is improved.