• Laser & Optoelectronics Progress
  • Vol. 58, Issue 20, 2007001 (2021)
Qi Wang*, Xiaopeng Wang, and Bohui Wang
Author Affiliations
  • School of Electronic and Information Engineering, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, China
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    DOI: 10.3788/LOP202158.2007001 Cite this Article Set citation alerts
    Qi Wang, Xiaopeng Wang, Bohui Wang. Echo Signal Denoising Based on Optimized Variational Mode Decomposition Algorithm[J]. Laser & Optoelectronics Progress, 2021, 58(20): 2007001 Copy Citation Text show less
    Flow chart of VMD denoising based on parameter optimization
    Fig. 1. Flow chart of VMD denoising based on parameter optimization
    Noise-free ultrasonic echo signal and frequency spectrum. (a) Echo signal; (b) frequency spectrum
    Fig. 2. Noise-free ultrasonic echo signal and frequency spectrum. (a) Echo signal; (b) frequency spectrum
    EMD modes and frequency spectra under noise-free signal. (a) EMD modes; (b) frequency spectra
    Fig. 3. EMD modes and frequency spectra under noise-free signal. (a) EMD modes; (b) frequency spectra
    VMD modes and frequency spectra under noise-free signal. (a) VMD modes; (b) frequency spectra
    Fig. 4. VMD modes and frequency spectra under noise-free signal. (a) VMD modes; (b) frequency spectra
    VMD modes and frequency spectra under noise-free signal when [k, α]=[4, 2500]. (a) VMD modes; (b) frequency spectra
    Fig. 5. VMD modes and frequency spectra under noise-free signal when [k, α]=[4, 2500]. (a) VMD modes; (b) frequency spectra
    VMD modes and frequency spectra under noise-free signal when [k, α]=[5, 2500]. (a) VMD modes; (b) frequency spectra
    Fig. 6. VMD modes and frequency spectra under noise-free signal when [k, α]=[5, 2500]. (a) VMD modes; (b) frequency spectra
    VMD modes and frequency spectra under noise-free signal when [k, α]=[6, 2500]. (a) VMD modes; (b) frequency spectra
    Fig. 7. VMD modes and frequency spectra under noise-free signal when [k, α]=[6, 2500]. (a) VMD modes; (b) frequency spectra
    Ultrasonic echo signal and frequency spectrum after adding white Gaussian noise with SNR of 20 dB. (a) Echo signal; (b) frequency spectrum
    Fig. 8. Ultrasonic echo signal and frequency spectrum after adding white Gaussian noise with SNR of 20 dB. (a) Echo signal; (b) frequency spectrum
    VMD modes and frequency spectra under white Gaussian noise. (a) VMD modes; (b) frequency spectra
    Fig. 9. VMD modes and frequency spectra under white Gaussian noise. (a) VMD modes; (b) frequency spectra
    EMD modes and frequency spectra under white Gaussian noise. (a) EMD modes; (b) frequency spectra
    Fig. 10. EMD modes and frequency spectra under white Gaussian noise. (a) EMD modes; (b) frequency spectra
    Ultrasonic echo signal and frequency spectrum after adding FFN1 with SNR of 15 dB. (a) Echo signal; (b) frequency spectrum
    Fig. 11. Ultrasonic echo signal and frequency spectrum after adding FFN1 with SNR of 15 dB. (a) Echo signal; (b) frequency spectrum
    VMD modes and frequency spectra under FFN1. (a) VMD modes; (b) frequency spectra
    Fig. 12. VMD modes and frequency spectra under FFN1. (a) VMD modes; (b) frequency spectra
    EMD modes and frequency spectra under FFN1. (a) EMD modes; (b) frequency spectra
    Fig. 13. EMD modes and frequency spectra under FFN1. (a) EMD modes; (b) frequency spectra
    Ultrasonic echo signal and frequency spectrum after adding FFN2 with SNR of 17 dB. (a) Echo signal; (b) frequency spectrum
    Fig. 14. Ultrasonic echo signal and frequency spectrum after adding FFN2 with SNR of 17 dB. (a) Echo signal; (b) frequency spectrum
    VMD modes and frequency spectra under FFN2. (a) VMD modes; (b) frequency spectra
    Fig. 15. VMD modes and frequency spectra under FFN2. (a) VMD modes; (b) frequency spectra
    EMD modes and frequency spectra under FFN2. (a) EMD modes; (b) frequency spectra
    Fig. 16. EMD modes and frequency spectra under FFN2. (a) EMD modes; (b) frequency spectra
    Denoised reconstructed signal and frequency spectrum when white Gaussian noise is added. (a) Reconstructed signal; (b) frequency spectrum
    Fig. 17. Denoised reconstructed signal and frequency spectrum when white Gaussian noise is added. (a) Reconstructed signal; (b) frequency spectrum
    Denoised reconstructed signal and frequency spectrum when FFN1 is added. (a) Reconstructed signal; (b) frequency spectrum
    Fig. 18. Denoised reconstructed signal and frequency spectrum when FFN1 is added. (a) Reconstructed signal; (b) frequency spectrum
    Denoised reconstructed signal and frequency spectrum when FFN2 is added. (a) Reconstructed signal; (b) frequency spectrum
    Fig. 19. Denoised reconstructed signal and frequency spectrum when FFN2 is added. (a) Reconstructed signal; (b) frequency spectrum
    Noisy signal and frequency spectrum in experiment. (a) Noisy signal; (b) frequency spectrum
    Fig. 20. Noisy signal and frequency spectrum in experiment. (a) Noisy signal; (b) frequency spectrum
    VMD modes and frequency spectra of noisy signal. (a) VMD modes; (b) frequency spectra
    Fig. 21. VMD modes and frequency spectra of noisy signal. (a) VMD modes; (b) frequency spectra
    EMD modes and frequency spectra of noisy signal. (a) EMD modes; (b) frequency spectra
    Fig. 22. EMD modes and frequency spectra of noisy signal. (a) EMD modes; (b) frequency spectra
    IMF componentCorrelation coefficient
    IMF10.9443
    IMF20.0076
    IMF30.0124
    Table 1. Correlations between IMF components and original signal
    Denoising methodWavelet thresholdEMD+wavelet thresholdEEMD+wavelet thresholdVMD+wavelet thresholdProposed method
    SNR10.075412.806413.202413.321414.2134
    MSE0.11230.08630.06390.05960.0396
    Table 2. Performance comparisons of 5 denoising methods
    Qi Wang, Xiaopeng Wang, Bohui Wang. Echo Signal Denoising Based on Optimized Variational Mode Decomposition Algorithm[J]. Laser & Optoelectronics Progress, 2021, 58(20): 2007001
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