Statistical analysis of synchrosqueezed transforms

Yang, Haizhao

doi:10.1016/j.acha.2017.01.001

Title: Statistical analysis of synchrosqueezed transforms

Journal Article · Thu Nov 01 00:00:00 EDT 2018 · Applied and Computational Harmonic Analysis

DOI:https://doi.org/10.1016/j.acha.2017.01.001· OSTI ID:1896340

Synchrosqueezed transforms are non-linear processes for a sharpened time–frequency representation of wave-like components. They are efficient tools for identifying and analyzing wave-like components from their superposition. This paper is concerned with the statistical properties of compactly supported synchrosqueezed transforms for wave-like components embedded in a generalized Gaussian random process in multidimensional spaces. Guided by the theoretical analysis of these properties, new numerical implementations are proposed to reduce the noise fluctuations of these transforms on noisy data. A MATLAB package SynLab together with several heavily noisy examples is provided to support these theoretical claims.

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Research Organization:: Stanford Univ., CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: FC02-13ER26134/DE-SC0009409; SC0009409

OSTI ID:: 1896340

Alternate ID(s):: OSTI ID: 1611205; OSTI ID: 1701852

Journal Information:: Applied and Computational Harmonic Analysis, Journal Name: Applied and Computational Harmonic Analysis Vol. 45 Journal Issue: 3; ISSN 1063-5203

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 31 works

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References (38)

Multitaper Time-Frequency Reassignment for Nonstationary Spectrum Estimation and Chirp Enhancement Xiao, Jun; Flandrin, Patrick IEEE Transactions on Signal Processing, Vol. 55, Issue 6 https://doi.org/10.1109/TSP.2007.893961	journal	June 2007
Crystal Image Analysis Using 2D Synchrosqueezed Transforms Yang, Haizhao; Lu, Jianfeng; Ying, Lexing Multiscale Modeling & Simulation, Vol. 13, Issue 4 https://doi.org/10.1137/140955872	journal	January 2015
Differential reassignment Chassande-Mottin, E.; Daubechies, I.; Auger, F. IEEE Signal Processing Letters, Vol. 4, Issue 10 https://doi.org/10.1109/97.633772	journal	October 1997
Estimating and interpreting the instantaneous frequency of a signal. I. Fundamentals Boashash, B. Proceedings of the IEEE, Vol. 80, Issue 4 https://doi.org/10.1109/5.135376	journal	April 1992
Time-Frequency Reassignment and Synchrosqueezing: An Overview Auger, Francois; Flandrin, Patrick; Lin, Yu-Ting IEEE Signal Processing Magazine, Vol. 30, Issue 6 https://doi.org/10.1109/MSP.2013.2265316	journal	November 2013
Non-parametric and adaptive modelling of dynamic periodicity and trend with heteroscedastic and dependent errors Chen, Yu-Chun; Cheng, Ming-Yen; Wu, Hau-Tieng Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 76, Issue 3 https://doi.org/10.1111/rssb.12039	journal	October 2013
Applications of the synchrosqueezing transform in seismic time-frequency analysis Herrera, Roberto H.; Han, Jiajun; van der Baan, Mirko GEOPHYSICS, Vol. 79, Issue 3 https://doi.org/10.1190/geo2013-0204.1	journal	May 2014
A unified approach to the change of resolution: space and gray-level Peleg, S.; Werman, M.; Rom, H. IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 11, Issue 7 https://doi.org/10.1109/34.192468	journal	July 1989
A generalized synchrosqueezing transform for enhancing signal time–frequency representation Li, Chuan; Liang, Ming Signal Processing, Vol. 92, Issue 9 https://doi.org/10.1016/j.sigpro.2012.02.019	journal	September 2012
Combining 2D synchrosqueezed wave packet transform with optimization for crystal image analysis Lu, Jianfeng; Wirth, Benedikt; Yang, Haizhao Journal of the Mechanics and Physics of Solids, Vol. 89 https://doi.org/10.1016/j.jmps.2016.01.002	journal	April 2016
Real-time dynamics acquisition from irregular samples — With application to anesthesia evaluation Chui, Charles K.; Lin, Yu-Ting; Wu, Hau-Tieng Analysis and Applications, Vol. 14, Issue 04 https://doi.org/10.1142/S0219530515500165	journal	April 2016
Proper complex random processes with applications to information theory Neeser, F. D.; Massey, J. L. IEEE Transactions on Information Theory, Vol. 39, Issue 4 https://doi.org/10.1109/18.243446	journal	July 1993
Spectral estimation-What is new? What is next? Tary, Jean Baptiste; Herrera, Roberto Henry; Han, Jiajun Reviews of Geophysics, Vol. 52, Issue 4 https://doi.org/10.1002/2014RG000461	journal	October 2014
Engineering analysis of biological variables: An example of blood pressure over 1 day Huang, Wei; Shen, Zheng; Huang, Norden E. Proceedings of the National Academy of Sciences, Vol. 95, Issue 9 https://doi.org/10.1073/pnas.95.9.4816	journal	April 1998
Synchrosqueezed Wave Packet Transform for 2D Mode Decomposition Yang, Haizhao; Ying, Lexing SIAM Journal on Imaging Sciences, Vol. 6, Issue 4 https://doi.org/10.1137/120891113	journal	January 2013
Detecting highly oscillatory signals by chirplet path pursuit Candès, Emmanuel J.; Charlton, Philip R.; Helgason, Hannes Applied and Computational Harmonic Analysis, Vol. 24, Issue 1 https://doi.org/10.1016/j.acha.2007.04.003	journal	January 2008
Evaluating Physiological Dynamics via Synchrosqueezing: Prediction of Ventilator Weaning Wu, Hau-Tieng; Hseu, Shu-Shua; Bien, Mauo-Ying IEEE Transactions on Biomedical Engineering, Vol. 61, Issue 3 https://doi.org/10.1109/TBME.2013.2288497	journal	March 2014
On instantaneous amplitude and phase of signals Picinbono, B. IEEE Transactions on Signal Processing, Vol. 45, Issue 3 https://doi.org/10.1109/78.558469	journal	March 1997
Synchrosqueezed wave packet transforms and diffeomorphism based spectral analysis for 1D general mode decompositions Yang, Haizhao Applied and Computational Harmonic Analysis, Vol. 39, Issue 1 https://doi.org/10.1016/j.acha.2014.08.004	journal	July 2015
Spectrum estimation and harmonic analysis Thomson, D. J. Proceedings of the IEEE, Vol. 70, Issue 9 https://doi.org/10.1109/PROC.1982.12433	journal	January 1982
Instantaneous frequency and wave shape functions (I) Wu, Hau-tieng Applied and Computational Harmonic Analysis, Vol. 35, Issue 2 https://doi.org/10.1016/j.acha.2012.08.008	journal	September 2013
Synchrosqueezed Curvelet Transform for Two-Dimensional Mode Decomposition Yang, Haizhao; Ying, Lexing SIAM Journal on Mathematical Analysis, Vol. 46, Issue 3 https://doi.org/10.1137/130939912	journal	January 2014
Second-Order Synchrosqueezing Transform or Invertible Reassignment? Towards Ideal Time-Frequency Representations Oberlin, Thomas; Meignen, Sylvain; Perrier, Valerie IEEE Transactions on Signal Processing, Vol. 63, Issue 5 https://doi.org/10.1109/TSP.2015.2391077	journal	March 2015
Best chirplet chain: Near-optimal detection of gravitational wave chirps Chassande-Mottin, Éric; Pai, Archana Physical Review D, Vol. 73, Issue 4 https://doi.org/10.1103/PhysRevD.73.042003	journal	February 2006
The multivariate complex normal distribution-a generalization van den Bos, A. IEEE Transactions on Information Theory, Vol. 41, Issue 2 https://doi.org/10.1109/18.370165	journal	March 1995
Quantitative Canvas Weave Analysis Using 2-D Synchrosqueezed Transforms: Application of time-frequency analysis to art investigation Yang, Haizhao; Lu, Jianfeng; Brown, William P. IEEE Signal Processing Magazine, Vol. 32, Issue 4 https://doi.org/10.1109/MSP.2015.2406882	journal	July 2015
Improving the readability of time-frequency and time-scale representations by the reassignment method Auger, F.; Flandrin, P. IEEE Transactions on Signal Processing, Vol. 43, Issue 5 https://doi.org/10.1109/78.382394	journal	May 1995
The Synchrosqueezing algorithm for time-varying spectral analysis: Robustness properties and new paleoclimate applications Thakur, Gaurav; Brevdo, Eugene; Fučkar, Neven S. Signal Processing, Vol. 93, Issue 5 https://doi.org/10.1016/j.sigpro.2012.11.029	journal	May 2013
Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool Daubechies, Ingrid; Lu, Jianfeng; Wu, Hau-Tieng Applied and Computational Harmonic Analysis, Vol. 30, Issue 2 https://doi.org/10.1016/j.acha.2010.08.002	journal	March 2011
Analysis and visualization of multiply oriented lattice structures by a two-dimensional continuous wavelet transform Singer, H. M.; Singer, I. Physical Review E, Vol. 74, Issue 3 https://doi.org/10.1103/PhysRevE.74.031103	journal	September 2006
Ideal spatial adaptation by wavelet shrinkage Donoho, David L.; Johnstone, Iain M. Biometrika, Vol. 81, Issue 3 https://doi.org/10.1093/biomet/81.3.425	journal	September 1994
Using synchrosqueezing transform to discover breathing dynamics from ECG signals Wu, Hau-Tieng; Chan, Yi-Hsin; Lin, Yu-Ting Applied and Computational Harmonic Analysis, Vol. 36, Issue 2 https://doi.org/10.1016/j.acha.2013.07.003	journal	March 2014
The monogenic synchrosqueezed wavelet transform: a tool for the decomposition/demodulation of AM–FM images Clausel, Marianne; Oberlin, Thomas; Perrier, Valérie Applied and Computational Harmonic Analysis, Vol. 39, Issue 3 https://doi.org/10.1016/j.acha.2014.10.003	journal	November 2015
Seismic data decomposition into spectral components using regularized nonstationary autoregression Fomel, Sergey GEOPHYSICS, Vol. 78, Issue 6 https://doi.org/10.1190/geo2013-0221.1	journal	November 2013
Synchrosqueezing-Based Recovery of Instantaneous Frequency from Nonuniform Samples Thakur, Gaurav; Wu, Hau-Tieng SIAM Journal on Mathematical Analysis, Vol. 43, Issue 5 https://doi.org/10.1137/100798818	journal	January 2011
Some Considerations on Physical Analysis of data Wu, Zhaohua; Huang, Norden E.; Chen, Xianyao Advances in Adaptive Data Analysis, Vol. 03, Issue 01n02 https://doi.org/10.1142/S1793536911000660	journal	April 2011
De-noising by soft-thresholding Donoho, D. L. IEEE Transactions on Information Theory, Vol. 41, Issue 3 https://doi.org/10.1109/18.382009	journal	May 1995
Wave and Group Transformation by a Hilbert Spectrum Veltcheva, Albena Dimitrova Coastal Engineering Journal, Vol. 44, Issue 4 https://doi.org/10.1142/S057856340200055X	journal	December 2002

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