Skip to main content
×
Home
    • Aa
    • Aa

Multidimensional Iterative Filtering Method for the Decomposition of High–Dimensional Non–Stationary Signals

  • Antonio Cicone (a1) and Haomin Zhou (a2)
Abstract
Abstract

Iterative Filtering (IF) is an alternative technique to the Empirical Mode Decomposition (EMD) algorithm for the decomposition of non–stationary and non–linear signals. Recently in [3] IF has been proved to be convergent for any L 2 signal and its stability has been also demonstrated through examples. Furthermore in [3] the so called Fokker–Planck (FP) filters have been introduced. They are smooth at every point and have compact supports. Based on those results, in this paper we introduce the Multidimensional Iterative Filtering (MIF) technique for the decomposition and time–frequency analysis of non–stationary high–dimensional signals. We present the extension of FP filters to higher dimensions. We prove convergence results under general sufficient conditions on the filter shape. Finally we illustrate the promising performance of MIF algorithm, equipped with high–dimensional FP filters, when applied to the decomposition of two dimensional signals.

Copyright
Corresponding author
*Corresponding author. Email addresses: antonio.cicone@univaq.it (A. Cicone), hmzhou@math.gatech.edu (H. M. Zhou)
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1] F. Auger and P. Flandrin , Improving the readability of time-frequency and time-scale representations by the reassignment method, IEEE T. Signal Proces., 43 (1995), pp. 10681089.

[2] B. Boashash , Estimating and interpreting the instantaneous frequency of a signal. I. fundamentals, P. IEEE, 80 (1992), pp. 520538.

[3] A. Cicone , J. Liu and H. Zhou , Adaptive local iterative filtering for signal decomposition and instantaneous frequency analysis, Appl. Comput. Harmon. A., 41 (2016), pp. 384411, http://dx.doi.org/10.1016/j.acha.2016.03.001.

[4] A. Cicone , J. Liu and H. Zhou , Hyperspectral chemical plume detection algorithms based on multidimensional iterative filtering decomposition, Phil. Trans. R. Soc. A, 374 (2016), doi: 10.1098/rsta.2015.0196.

[5] M. Clausel , T. Oberlin and V. Perrier , The monogenic synchrosqueezed wavelet transform: a tool for the decomposition/demodulation of am–fmimages, Appl. Comput. Harmon. A., 39 (2015), pp. 450486.

[7] I. Daubechies , J. Lu and H. T. Wu , Synchrosqueezed wavelet transforms: an empirical mode decomposition-like tool, Appl. Comput. Harmon. A., 30 (2011), pp. 243261.

[8] I. Daubechies , Y. G. Wang and H. T. Wu , Conceft: concentration of frequency and time via a multitapered synchrosqueezed transform, Phil. Trans. R. Soc. A, 374 (2016), pp. 20150193.

[9] K. Dragomiretskiy and D. Zosso , Variational mode decomposition, IEEE T. Signal. Proces., 62 (2014), pp. 531544.

[10] J. Gilles , Empirical wavelet transform, IEEE T. Signal. Proces., 61 (2013), pp. 39994010.

[11] J. Gilles , G. Tran and S. Osher , 2D empirical transforms, wavelets, ridgelets, and curvelets revisited, SIAM J. Imaging Sci., 7 (2014), pp. 157186.

[13] T. Y. Hou and Z. Shi , Adaptive data analysis via sparse time-frequency representation, Adv. Adapt. Data Anal., 3 (2011), pp. 128.

[14] N. E. Huang , Z. Shen , S. R. Long , M. C. Wu , H. H. Shih , Q. Zheng , N. C. Yen , C. C. Tung and H. H. Liu , The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis, Proc. Royal Soc. London. Ser. A, 454 (1998), pp. 903995.

[15] E. Kalnay , M. Kanamitsu , R. Kistler , W. Collins , D. Deaven , L. Gandin , M. Iredell , S. Saha , G. White and J. Woollen , et al., The ncep/ncar 40–year reanalysis project, Bulletin of the American meteorological Society, 77 (1996), pp. 437471.

[17] L. Lin , Y. Wang , and H. Zhou , Iterative filtering as an alternative algorithm for empirical mode decomposition, Adv. Adapt. Data Anal., 1 (2009), pp. 543560.

[18] J. V. Lorenzo-Ginori , An approach to the 2d Hilbert transform for image processing applications, in International Conference Image Analysis and Recognition, Springer, 2007, pp. 157165.

[19] D. Manolakis and G. Shaw , Detection algorithms for hyperspectral imaging applications, IEEE Signal Proc. Mag., 19 (2002), pp. 2943.

[22] I. W. Selesnick , Resonance-based signal decomposition: A new sparsity-enabled signal analysis method, Sig. Proc., 91 (2011), pp. 27932809.

[23] H. Takeda , S. Farsiu and P. Milanfar , Kernel regression for image processing and reconstruction, IEEE T. Image. Process., 16 (2007), pp. 349366.

[24] D. Wei and A. Bovik , On the instantaneous frequencies of multicomponent am-fm signals, IEEE Signal Proc. Let., 5 (1998), pp. 8486.

[25] H. T. Wu , P. Flandrin and I. Daubechies , One or two frequencies? the synchrosqueezing answers, Adv. Adap. Data An., 3 (2011), pp. 2939.

[26] Z. Wu and N. E. Huang , Ensemble empirical mode decomposition: a noise-assisted data analysis method, Adv. Adap. Data An., 1 (2009), pp. 141.

[27] Z. Wu , N. E. Huang and X. Chen , The multi–dimensional ensemble empirical mode decomposition method, Adv. Adap. Data An., 1 (2009), pp. 339372.

[28] H. Yang and L. Ying , Synchrosqueezed wave packet transform for two–dimensional mode decomposition, SIAM J. Imaging Sci., 6 (2013), pp. 19792009.

[29] H. Yang and L. Ying , Synchrosqueezed curvelet transform for two–dimensional mode decomposition, SIAM J. Math. Anal., 46 (2014), pp. 20522083.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Numerical Mathematics: Theory, Methods and Applications
  • ISSN: 1004-8979
  • EISSN: 2079-7338
  • URL: /core/journals/numerical-mathematics-theory-methods-and-applications
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords:

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 9 *
Loading metrics...

Abstract views

Total abstract views: 23 *
Loading metrics...

* Views captured on Cambridge Core between 9th May 2017 - 22nd May 2017. This data will be updated every 24 hours.