压缩小波变换和非线性阈值技术压制磁共振尖峰噪声方法研究

地面磁共振是一种新的地球物理探测方法,能够通过探测地下水中氢质子丰度获取地下水含量、孔隙度等水文地质信息.然而,磁共振信号甚为微弱,仅达到纳伏级(10~(-9)V),极易受到噪声干扰.其中,尖峰噪声对磁共振信号影响最为严重,亟待研究有效的噪声抑制方法.小波多尺度分解硬阈值是近两年国际磁共振领域专家提出的尖峰噪声有效消除方法,但硬阈值算法设定阈值的固有缺陷会引发信号震荡,出现伪吉布斯效应,导致信号损失.基于此,本文提出压缩小波变换(Synchrosqueezing Wavelet Transform,SWT)和非线性國值处理(Nonlinear Thresholding,NT)算法联合消除磁共振信号尖峰噪声干扰.首先选择Morlet小波作为基小波,使得信号与噪声数据具有更高的时频集中性,利于尖峰噪声消除.其次,基于压缩小波系数进行非线性处理,可以弥补利用硬阈值和软阈值进行噪声消除时所引起的信号损失.仿真数据和实际数据结果表明,SWT联合NT方法可以利用单次采集数据有效消除尖峰噪声干扰并还原信号.本文提出的消噪方法将为磁共振数据后续反演解释,如多指数弛豫反演,奠定坚实的基础.

Synchrosqueezing wavelet transform and nonlinear thresholding algorithm for despiking of surface NMR signals

Surface Nuclear Magnetic Resonance (SNMR) is a new geophysical technique to measure the abundance of hydrogen nuclei in the subsurface. However, the SNMR signal is as weak as 10^-9 V and easy to be disturbed by noise, in which spikes are one of the most important sources for SNMR to be overcome. The multi-scale wavelet decomposition is one of the most effective methods to remove this noise proposed by the international scholars in recent years. However, the hard threshold algorithm which generates the pseudo-Gibbs phenomenon leads the loss of SNMR signal. Thus, to construct an efficient method to reject spikes, we developed a Synchrosqueezing Wavelet Transform (SWT) and Nonlinear Thresholding (NT) algorithm. In this method, Morlet is the basic wavelet which permits to make signal and spikes more concentrated, respectively. The synchrosqueezing wavelet coefficient used by the NT algorithm which can make up for the lost SNMR signal caused by hard threshold or soft threshold. The tests on simulating and actual data show that the SWTNT algorithm can remove spikes and restore signal using the data by only one sampling. The SNMR signal can facilitate the subsequent inversion and interpretation better after the noise is suppressed by this method.