基于小波变换的低场核磁共振信号去噪方法的研究进展

低场核磁共振（low-field Nuclear Magnetic Resonance，low-field NMR）技术因其自身具有的独特优越性常被应用于极端条件下的测量，而且由于其采用的是永磁体，因而采集到的信号信噪比常常较低，在很大程度上影响了测量值的准确性.因此，如何去除混杂在信号中的加性高斯白噪声增加测量值的可靠性显得尤为重要.针对这一问题，国内外学者相继提出了众多优秀的去噪方法，其核心都是在不损失含噪信号中有效信息的基础上滤除掉夹杂在其中的噪声信号.本文在基于对小波变换理论分析的基础上，介绍了3种目前较为流行的用于低场核磁共振信号去噪的方法，分别是小波阈值去噪、模极大值去噪和小波系数相关性去噪，并给出了用于评价去噪效果的四个参数及其计算方法.

Wavelet Transform-Based Signal Denoising in Low-Field NMR

Low-field NMR often uses permanent magnet. The signals obtained contain high level of white Gaussian noises, and have low signal-to-noise ratio (SNR). In recent years, many denoising methods have been proposed for low-field NMR measurements. Most of these methods can remove noises without losing useful information contained in the original signals. Wavelet transform is the most popular denoising method among them. In this paper, we first introduced the theory of wavelet transform analysis, followed by review of three wavelet transform denoising methods for low-field NMR, namely the wavelet threshold method, the wavelet transform modulus maximum method and the correlation of wavelet coefficient method. Finally, we showed that four parameters could be calculated to evaluate the denoising performance.