- Volume 22 Issue 2
DOI QR Code
Signal Reconstruction by Synchrosqueezed Wavelet Transform
- Park, Minsu (Department of Statistics, Seoul National University) ;
- Oh, Hee-Seok (Department of Statistics, Seoul National University) ;
- Kim, Donghoh (Department of Applied Mathematics, Sejong University)
- Received : 2015.01.04
- Accepted : 2015.02.20
- Published : 2015.03.31
This paper considers the problem of reconstructing an underlying signal from noisy data. This paper presents a reconstruction method based on synchrosqueezed wavelet transform recently developed for multiscale representation. Synchrosqueezed wavelet transform based on continuous wavelet transform is efficient to estimate the instantaneous frequency of each component that consist of a signal and to reconstruct components. However, an objective selection method for the optimal number of intrinsic mode type functions is required. The proposed method is obtained by coupling the synchrosqueezed wavelet transform with cross-validation scheme. Simulation studies and musical instrument sounds are used to compare the empirical performance of the proposed method with existing methods.
Supported by : National Research Foundation of Korea (NRF)
- Allen, J. B. and Rabiner, L. R. (1977). A unified approach to short-time Fourier analysis and synthesis, Proceedings of the IEEE, 65, 1558-1564. https://doi.org/10.1109/PROC.1977.10770
- Auger, F. and Flandrin, P. (1995). Improving the readability of time-frequency and time-scale representations by the reassignment method, IEEE Transactions on Signal Processing, 43, 1068-1089. https://doi.org/10.1109/78.382394
- Claasen, T. and Mecklenbrauker, W. F. C. (1980). The Wigner distribution: A tool for time frequency signal analysis, Philips Journal of Research, 35, 217-250.
- Daubechies, I., Lu, J. and Wu, H. T. (2011). Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool, Applied and Computational Harmonic Analysis, 30, 243-261. https://doi.org/10.1016/j.acha.2010.08.002
- Dempster, A. P., Laird, N. M. and Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society: Series B, 39, 1-38.
- Donoho, D. L. and Johnstone, I. M. (1995). Adapting to unknown smoothing via wavelet shrinkage, Journal of the American Statistical Association, 90, 1200-1224. https://doi.org/10.1080/01621459.1995.10476626
- Flandrin, P. (1999). Time-Frequency/Time-Scale Analysis, Academic Press.
- Huang, N. E., Shen, Z., Long, S. R., Wu, M. L., Shih, H. H., Zheng, Q., Yen, N. C., Tung, C. C. and Liu, H. H. (1998). The empirical mode decomposition and Hilbert spectrum for nonlinear and nonstationary time series analysis, Proceedings of the Royal Society of London A, 454, 903-995. https://doi.org/10.1098/rspa.1998.0193
- Kim, D., Lee, Y. and Oh, H.-S. (2006). Hierarchical-likelihood-based wavelet method for denoting signals with missing data, IEEE Signal Processing Letters, 13, 361-364. https://doi.org/10.1109/LSP.2006.871713
- Lee, T. C. M. and Meng, X. L. (2005). A self-consistent wavelet method for denoising images with missing pixels, In Proceedings of the 30th IEEE International Conference on Acoustics, Speech, and Signal Processing, 2, 41-44.
- Mallat, S. (1999). A Wavelet Tour of Signal Processing, Academic Press.
- Meignen, S., Oberlin, T. and McLaughlin, S. (2012). A new algorithm for multicomponent signals analysis based on synchrosqueezing: With an application to signal sampling and denoising, IEEE Transactions on Signal Processing, 60, 5787-5798. https://doi.org/10.1109/TSP.2012.2212891
- Nason, G. P. (1996). Wavelet shrinkage by cross-validation, Journal of the Royal Statistical Society: Series B, 58, 463-479.
- Oh, H.-S., Kim, D. and Lee, Y. (2009). Cross-validated wavelet shrinkage, Computational Statistics, 24, 497-512. https://doi.org/10.1007/s00180-008-0143-7
- Thakur, G., Brevdo, E., Fuckar, N. S. and Wu, H.-T. (2013). The synchrosqueezing algorithm for time-varying spectral analysis: Robustness properties and new paleoclimate applications, Signal Processing, 93, 1079-1094. https://doi.org/10.1016/j.sigpro.2012.11.029
- Thakur, G. and Wu, H.-T. (2011). Synchrosqueezing-based recovery of instantaneous frequency from nonuniform samples, SIAM Journal on Mathematical Analysis, 43, 2078-2095. https://doi.org/10.1137/100798818
- Yang, H. and Ying, L. (2013). Synchrosqueezed wave packet transform for 2D mode decomposition, SIAM Journal on Imaging Sciences, 6, 1979-2009. https://doi.org/10.1137/120891113