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Conceptualization, B.T. and H.L.; methodology, X.L.; software, X.L.; validation, H.D. and L.W.; formal analysis, L.W. and H.Z.; investigation, X.L.; resources, L.W. and H.Z.; data curation, H.D. and L.W.; writing—original draft preparation, X.L., L.W. and B.T.; writing—review and editing, X.L., H.D. and B.T.; visualization, X.L. and H.D.; supervision, H.L.; project administration, B.T.; funding acquisition, B.T. All authors have read and agreed to the published version of the manuscript.
Figure 1. Denoising results of the MP algorithm when SNR = −5.98 dB: (a) noisy data and reconstructed power-line harmonics by MP and HMC; (c) is the corresponding spectrum. (b) After removing the harmonics, the MRS signal is extracted by MP and HMC; (d) is the corresponding spectrum.
Figure 1. Denoising results of the MP algorithm when SNR = −5.98 dB: (a) noisy data and reconstructed power-line harmonics by MP and HMC; (c) is the corresponding spectrum. (b) After removing the harmonics, the MRS signal is extracted by MP and HMC; (d) is the corresponding spectrum.
Figure 2. Denoising results of the MP algorithm when SNR = −20.05 dB: (a) noisy data and reconstructed power-line harmonics by MP and HMC; (c) is the corresponding spectrum. (b) After removing the harmonics, the MRS signal is extracted by MP and HMC; (d) is the corresponding spectrum.
Figure 2. Denoising results of the MP algorithm when SNR = −20.05 dB: (a) noisy data and reconstructed power-line harmonics by MP and HMC; (c) is the corresponding spectrum. (b) After removing the harmonics, the MRS signal is extracted by MP and HMC; (d) is the corresponding spectrum.
Figure 3. Comparison of denoising results under different fl: (a) Δf = 1 Hz, (b) is the corresponding spectrum; (c) Δf = 3 Hz, (d) is the corresponding spectrum; (e) Δf = 5 Hz, (f) is the corresponding spectrum.
Figure 3. Comparison of denoising results under different fl: (a) Δf = 1 Hz, (b) is the corresponding spectrum; (c) Δf = 3 Hz, (d) is the corresponding spectrum; (e) Δf = 5 Hz, (f) is the corresponding spectrum.
Figure 4. Fitting error maps of E0 and T2* after denoising by the MP algorithm under different SNR. (a) E0, (b) T2*.
Figure 4. Fitting error maps of E0 and T2* after denoising by the MP algorithm under different SNR. (a) E0, (b) T2*.
Figure 5. Comparison of the denoising results of the MP, SSA, and HMC algorithms under different SNRs: (a) SNR = −10.7 dB, (b) is the corresponding spectrum; (c) SNR = −12.8 dB, (d) is the corresponding spectrum; (e) SNR = −14.9 dB, (f) is the corresponding spectrum.
Figure 5. Comparison of the denoising results of the MP, SSA, and HMC algorithms under different SNRs: (a) SNR = −10.7 dB, (b) is the corresponding spectrum; (c) SNR = −12.8 dB, (d) is the corresponding spectrum; (e) SNR = −14.9 dB, (f) is the corresponding spectrum.
Figure 6. Comparison of denoising reuslts of the MP, SSA, and HMC algorithms with a frequency difference of 1, 3, and 5 Hz: (a) Δf = 1 Hz, (b) is the corresponding spectrum; (c) Δf = 3 Hz, (d) is the corresponding spectrum; (e) Δf = 5 Hz, (f) is the corresponding spectrum.
Figure 6. Comparison of denoising reuslts of the MP, SSA, and HMC algorithms with a frequency difference of 1, 3, and 5 Hz: (a) Δf = 1 Hz, (b) is the corresponding spectrum; (c) Δf = 3 Hz, (d) is the corresponding spectrum; (e) Δf = 5 Hz, (f) is the corresponding spectrum.
Figure 7. Comparison of denoising results of the MP, SSA, and HMC algorithms with T2* of 200, 300, and 400 ms: (a) T2* = 200 ms, (b) is the corresponding spectrum; (c) T2* = 300 ms, (d) is the corresponding spectrum; (e) T2* = 400 ms, (f) is the corresponding spectrum.
Figure 7. Comparison of denoising results of the MP, SSA, and HMC algorithms with T2* of 200, 300, and 400 ms: (a) T2* = 200 ms, (b) is the corresponding spectrum; (c) T2* = 300 ms, (d) is the corresponding spectrum; (e) T2* = 400 ms, (f) is the corresponding spectrum.
Figure 8. Processing results of field-measured data: (a) the results processing with the MP, HMC, and SSA algorithms under the fifth pulse moment and the time domain waveform of SNR = −8.42 dB data, with (c) the corresponding spectrum, and (b) under the seventh pulse moment and the time domain waveform of SNR = −4.71 dB data, with (d) the corresponding spectrum.
Figure 8. Processing results of field-measured data: (a) the results processing with the MP, HMC, and SSA algorithms under the fifth pulse moment and the time domain waveform of SNR = −8.42 dB data, with (c) the corresponding spectrum, and (b) under the seventh pulse moment and the time domain waveform of SNR = −4.71 dB data, with (d) the corresponding spectrum.
Table 1. Denoising results under different T2*.
Table 1. Denoising results under different T2*.
T2*/ msSNR¯ / dBΔSNR / dBE0 / nVT2* / ms50−23.7135.33184.70 ± 18.3855.56 ± 6.43100−20.7135.30201.14 ± 15.41101.02 ± 10.14200−17.6434.91195.75 ± 9.16205.18 ± 14.86300−15.9534.99198.26 ± 6.40307.13 ± 11.67400−14.7033.43194.88 ± 4.26408.31 ± 11.11500−13.7235.55198.65 ± 3.39506.66 ± 10.76Table 2. Denoising results under different Larmor frequencies fl.
Table 2. Denoising results under different Larmor frequencies fl.
fl/ HzSNR¯ / dBΔSNR / dBE0 / nVT2* / ms2301−14.0024.46179.16 ± 40.57195.31 ± 46.742302−13.9128.25186.45 ± 34.16205.00 ± 32.122303−13.9330.19185.27 ± 26.25211.21 ± 29.782304−14.0432.05190.62 ± 8.72198.29 ± 8.602305−14.0233.79190.01 ± 7.98211.26 ± 8.222306−13.9832.71193.72 ± 6.61201.55 ± 7.76
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