A Novel End-to-End Framework for Low-SNR FID Signal Denoising via Rank-Sequential Truncated Tensor Decomposition

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Abstract
To address the challenges of extracting weak, rapidly decaying, and noise-corrupted free induction decay (FID) signals from Overhauser magnetometers, this study introduces the rank-sequential truncated tensor decomposition (RSTD) method for effective noise suppression and high signal-to-noise ratio (SNR) signal recovery in high-noise environments. The proposed approach involves acquiring multichannel FID signals using an equal-delay strategy and organizing them into a third-order tensor through data segmentation. Subsequently, the tensor undergoes a higher-order singular value decomposition combined with matrix rank decomposition, following a predefined modal decomposition sequence to enhance SNR. Comparative evaluations against conventional techniques, including singular value decomposition (SVD), principal component analysis (PCA) assisted SVD (C-PCASVD), and multilinear SVD (MLSVD), demonstrate that RSTD achieves a signal-to-noise improvement ratio (SNIR) of 40 dB across initial SNRs ranging from -20 dB to 0 dB. The method matches MLSVD in denoising efficacy while outperforming SVD and C-PCASVD by more than 10 dB in SNIR. In particular, the proposed method completes processing within 100 ms, representing more than 50% improvement in computational efficiency over MLSVD. These results confirm that the proposed method substantially improves real-time processing capabilities without compromising noise reduction performance.
Funding Information
  • National Natural Science Foundation of China (42274233)
  • Basic and Applied Basic Research Foundation of Guangdong Province (2025A1515011073)
  • Young Top-notch Talent Cultivation Program of Hubei Province (20223451006)

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