Translation-invariant Wavelet Denoising Method Based on a New Thresholding Function for Underwater Acoustic Measurement

수중 음향 측정을 위한 새로운 임계치 함수에 의한 TI 웨이블렛 잡음제거 기법

  • Published : 2006.11.20


Donoho et al. suggested a wavelet thresholding denoising method based on discrete wavelet transform. This paper proposes an improved denoising method using a new thresholding function based on translation-invariant wavelet for underwater acoustic measurement. The conventional wavelet thresholding denoising method causes Pseudo-Gibbs phenomena near singularities due to the lack of translation-invariant of the wavelet basis. To suppress Pseudo-Gibbs phenomena, a denoising method combining a new thresholding function based on the translation-invariant wavelet transform is proposed in this paper. The new thresholding function is a modified hard-thresholding to each node according to the discriminated threshold so as to reject unknown external noise and white gaussian noise. The experimental results show that the proposed method can effectively eliminate noise, extract characteristic information of radiated noise signals.


  1. Donoho, D. L. and Johnstone, I. M., 1994, 'Ideal Spatial Adaptation by Wavelet Shrinkage', Biometrika, Vol. 81, pp. 425-455
  2. Liu, G. and Qu, L., 2002, 'Study On Wavelet Adaptive-threshold Denoising Method', Signal Processing, Vol. 18, pp.509-512
  3. Donoho, D. L. and Johnstone, I. M., 1995, 'Adapting to Unknown Smoothness Via Wavelet Shrinkage', Journal of American Statistical Association, Vol. 12, pp.1200-1224
  4. Ma Xiaoyan, Yuan Junguan, and Xue Linguang, 2000, 'Signal Reconstruction Based on Mean Threshold Wavelet Packet De-noising', IEEE Proceeding of ICSP 2000, pp.387-390
  5. Ching, P. C., So, H. C. and Wu, S. Q., 1999, 'On Wavelet Denoising and Its Application To Time Delay Estimation', IEEE Trans. Signal Processing, Vol. 47, pp. 2879-2882
  6. Coifman, R. R. and Donoho, D. L., 1994, 'Translation-invariant De-noising', In Wavelets and Statistics, Springer Lecture Notes in Statistics 103, New York: Springer-Verlag, pp.125-150
  7. Bui, T. D. and Chen, G., 1998, 'Translation-invariant Denoising Using multiwavelets', IEEE Trans. Signal Processing, Vol. 46, pp.3414-3420
  8. Li Su, Guoliang Zhao and Renyan Zhang, 2005, 'Translation-invariant Wavelet De-noising Method with Improved Thresholding', IEEE Proceeding of ISCIT 2005, pp. 599-602
  9. Lee, P. H. and Yoon, J. R, 2005, 'Ship Radiated Noise Measurement Methods and Accuracy Analysis', Transactions of the Korean Society for Noise and Vibration Engineering, Vol. 15, No.3, pp.738-748
  10. Choi, J. Y. and Dho, K. C., 2001, 'A Study on the Denoising Method by Multi-threshold for Underwater Transient Noise Measurement', The Journal of the Acoustical Society of Korea, Vol. 21, No.6, pp. 5- 13
  11. Donoho, D. L., 1995, 'De-noising by Soft-thresholding', IEEE Trans. Information Theory, Vol. 41, No.3, pp.613-627