###### Abstract  
Magnetic resonance sounding (MRS) is a non-invasive, direct, and quantitative geophysical method for detecting groundwater, and has been widely used in groundwater survey, water resource assessment, and disaster water source forecasting. However, the MRS signal is weak (nV level) and highly susceptible to environmental noise, such as random noise and power-line harmonics, resulting in reduced quality of received data. Achieving reliable extraction of MRS signals under strong noise is difficult. To solve this problem, we propose a matching pursuit algorithm based on sparse decomposition theory for data noise suppression and MRS signal extraction. In accordance with the characteristics of the signal and noise, an oscillating atomic library is constructed as a sparse dictionary to realize signal sparse decomposition. A two-step denoising strategy is proposed to reconstruct the power-line harmonics and then extract the MRS signal. We simulated synthetic data with different signal-to-noise ratios (SNRs), relaxation times, and Larmor frequencies. Our results show that the proposed algorithm can effectively remove power-line harmonics and reduce random noise. SNR is significantly improved by up to 35.6 dB after denoising. The effectiveness and superiority of the proposed algorithm are further verified by the measured data and through comparison with the singular spectrum analysis algorithm and harmonic modeling cancellation algorithm. magnetic resonance sounding; matching pursuit; sparse decomposition; oscillatory atomic library +
Footnote †: journal: _Applied_  
between the detection and reference channels is large. [PERSON] et al. [5] compared the filtering performance of the Wiener filter and ANC algorithm, and the results showed that the filtering effect of the two is equivalent. Regarding the removal of power-line harmonics, [PERSON] et al. [10] proposed a method based on the combination of power-line harmonic modeling and multichannel Wiener filtering. [PERSON] et al. [11] proposed a combination of harmonic modeling and autocorrelation to suppress power-line harmonics and random noise. [PERSON] et al. [12] and [PERSON] et al. [13] proposed a removal algorithm for co-frequency harmonics (when a harmonic frequency is the same or similar to the Larmor frequency). [PERSON] et al. [14] introduced a frame-based denoising method based on multichannel Wiener filtering in the frequency domain. The results show that the frame-based method improves denoising when the harmonic noise has asynchronous variations and multiple sources. With regard to the suppression of random noise, [PERSON] et al. [15] used the sparse representation method to extract nuclear magnetic resonance signals. [PERSON] et al. [16] used time-frequency peak filtering to suppress random noise. [PERSON] et al. [17] proposed an approach for intensive sampling sparse reconstruction (ISSR) and kernel regression estimation (KRE) to suppress random noise. [PERSON] et al. [18] used maximum likelihood estimation (MLE) to estimate nuclear magnetic resonance (NMR) parameters and suppress random noise in MRS. In addition, an algorithm for noise suppression of MRS signals from a statistical perspective has been proposed. The empirical mode decomposition algorithm based on statistical optimization has been used to extract the attenuation trend of effective MRS signals, although it exerts a good effect only when the SNR is high [19]. The independent component analysis method has been adopted for the extraction of effective MRS signals under multisource mixed noise [20]. The singular spectrum analysis (SSA) method has been utilized for filtering and parameter estimation of MRS data, and has achieved good results [21]. The above analysis shows that various methods achieve certain effects on improving the SNR of MRS signals. However, due to the complexity of environmental noise and multisource characteristics, the noise suppression problem of MRS signals remains challenging. Matching pursuit (MP) was proposed by [PERSON] [22].