Improving the Signal-to-Noise-Ratio of Free Induction Decay Signals Using a New Multilinear Singular Value Decomposition-Based Filter

The free induction decay (FID) signal output by a proton precession magnetometer (PPM) is usually only of the microvolt level, and its frequency is proportional to the magnetic field strength. Therefore, obtaining a high signal-to-noise ratio (SNR) FID signal is crucial for improving the measurement accuracy of the magnetometer. The current gold standards for noise reduction in FID signals-singular value decomposition (SVD) and principal component analysis (PCA)-still have limited denoising capabilities, especially in cases with strong noise interference. In this study, a new noise-reduction algorithm for FID based on multilinear SVD (MLSVD) is proposed. First, equal delay-based multichannel data sampling is used to obtain multiple correlated signals, and thus, the obtained multiple signals are constructed as a third-order tensor; second, the MLSVD is employed to calculate and remove the noise singular value of the tensor; and third, canonical polyadic decomposition (CPD) is used to fuse the multichannel FID signal processed by MLSVD and eliminate signal noise, further improving the SNR. Subsequently, a PPM experimental test platform was constructed, and extensive simulation and practical comparison tests were conducted. The results show that, when the SNR is -10 dB, the noise-reduction effect of the MLSVD is about 9.12 dB higher than that of the SVD and about 8.15 dB higher than that of the PCA, with an overall increase of 28%. In an environment with strong noise interference-with an SNR of -30 dB-both PCA and SVD are no longer viable, while MLSVD can still effectively suppress noise, with a signal-to-noise improvement ratio (SNIR) being as high as 50.36 dB.