Signal collected from magnetic resonance sounding (MRS) instrument is only a few tens of nano-volt and susceptible to environmental noise, leading to a low signal-to-noise ratio. In addition, the accuracy of characteristic parameter extraction from MRS signal is seriously affected, and the resulting error of the subsequent inversion interpretation increases. In this paper, a fast fixed-point algorithm for independent component analysis (FastICA) is utilized to enhance the performance in the high noisy environment. First, the applicability of FastICA algorithm to noise cancellation of MRS signal is analyzed. Whether the mixed signal can be separated completely depends on the appropriate choice of nonlinear function in FastICA algorithm, moreover, the choice of nonlinear function is closely related to the Gaussian type of signal. Thus, in this process, the kurtoses of noise and full-wave MRS signal are calculated, and then the Gaussian type of signal is determined. Therefore based on the Gaussian type of signal, we can choose the corresponding nonlinear function applied to the FastICA algorithm in order to realize the effective separation of the mixed signals. Secondly, undetermined blind source separation is one of common problems of ICA. To cope with this tough situation, a digital orthogonal method is adopted to construct some extra observed signals combined with the existing observed one as the input signal of this algorithm. Hence, the digital orthogonal method can satisfy the application condition of ICA, i.e., the number of observed signal must be greater than or equal to that of source signal. This means that it is able to remove the application limitation of ICA when there is only one observed signal. Owing to the problem of variable amplitude of separated signals after ICA, it is crucial to recover the initial amplitude of the separated MRS signal, because it represents the amount of water content in the aquifer. Aiming at this problem, a spectrum correcting method is proposed. In frequency domain, the spectrum of separated MRS signal is restored into the original value that is the spectrum of observed signal at Larmor frequency, then transformed into time domain by inversing fast Fourier transform to obtain the desired MRS signal.
In the validation of the proposed algorithm, two tests are considered: simulation and field data processing. In the simulation case, the observed signal constructed by full-wave MRS signal and two power-line harmonics with different frequencies is the main processing object, and the proposed algorithm is utilized to realize the observed signal separated into ideal MRS signal and noise effectively. To verify the applicability of this proposed algorithm further, under the condition of different initial amplitudes and relaxation times, the characteristic parameters of separated MRS signal are extracted by this proposed algorithm and the corresponding relative fitting error is determined. The simulation results show that adopting this algorithm can effectively realize the separation of the noisy full-wave MRS signal. In addition, the relative errors of initial amplitude and relaxation time after data fitting are both within 5.00%. When compared with the denoising ability of some other classical algorithms, the performance of this proposed algorithm is superior. Finally, this algorithm is applied to the processing of the field data. The results indicate that power-line harmonics and other single-frequency interference contained in the MRS signal can be removed effectively.
