Multidimensional Iterative Filtering method for the decomposition of high-dimensional non-stationary signals

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 [1] IF has been proved to be convergent for any $L^2$ signal and its stability has been also showed through examples. Furthermore in [1] 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. And we present the extension of FP filters to higher dimensions. We illustrate the promising performance of MIF algorithm, equipped with high-dimensional FP filters, when applied to the decomposition of 2D signals. [1] A. Cicone, J. Liu, and H. Zhou, Adaptive local iterative filtering for signal decomposition and instantaneous frequency analysis, arXiv:1411.6051, 2014.

[1]  Norden E. Huang,et al.  The Multi-Dimensional Ensemble Empirical Mode Decomposition Method , 2009, Adv. Data Sci. Adapt. Anal..

[2]  Juan V. Lorenzo-Ginori,et al.  An Approach to the 2D Hilbert Transform for Image Processing Applications , 2007, ICIAR.

[3]  Norden E. Huang,et al.  Ensemble Empirical Mode Decomposition: a Noise-Assisted Data Analysis Method , 2009, Adv. Data Sci. Adapt. Anal..

[4]  A. Bovik,et al.  On the instantaneous frequencies of multicomponent AM-FM signals , 1998, IEEE Signal Processing Letters.

[5]  Boualem Boashash,et al.  Estimating and interpreting the instantaneous frequency of a signal. I. Fundamentals , 1992, Proc. IEEE.

[6]  Patrick Flandrin,et al.  Improving the readability of time-frequency and time-scale representations by the reassignment method , 1995, IEEE Trans. Signal Process..

[7]  Lexing Ying,et al.  Synchrosqueezed Curvelet Transform for Two-Dimensional Mode Decomposition , 2014, SIAM J. Math. Anal..

[8]  Dominique Zosso,et al.  Variational Mode Decomposition , 2014, IEEE Transactions on Signal Processing.

[9]  Peyman Milanfar,et al.  Kernel Regression for Image Processing and Reconstruction , 2007, IEEE Transactions on Image Processing.

[10]  Patrick Flandrin,et al.  One or Two frequencies? The Synchrosqueezing Answers , 2011, Adv. Data Sci. Adapt. Anal..

[11]  N. Huang,et al.  The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[12]  Valérie Perrier,et al.  The Monogenic Synchrosqueezed Wavelet Transform: A tool for the Decomposition/Demodulation of AM-FM images , 2012, ArXiv.

[13]  Lexing Ying,et al.  Synchrosqueezed Wave Packet Transform for 2D Mode Decomposition , 2013, SIAM J. Imaging Sci..

[14]  Stanley Osher,et al.  Empirical Transforms . Wavelets , Ridgelets and Curvelets revisited , 2013 .

[15]  Yang Wang,et al.  Iterative Filtering as an Alternative Algorithm for Empirical Mode Decomposition , 2009, Adv. Data Sci. Adapt. Anal..

[16]  Nelly Pustelnik,et al.  2D Hilbert-Huang Transform , 2014, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[17]  Yi Wang,et al.  ConceFT: concentration of frequency and time via a multitapered synchrosqueezed transform , 2015, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[18]  Ivan W. Selesnick,et al.  Resonance-based signal decomposition: A new sparsity-enabled signal analysis method , 2011, Signal Process..

[19]  Thomas S. Huang,et al.  Image processing , 1971 .

[20]  Nelly Pustelnik,et al.  A multicomponent proximal algorithm for Empirical Mode Decomposition , 2012, 2012 Proceedings of the 20th European Signal Processing Conference (EUSIPCO).

[21]  R. Reynolds,et al.  The NCEP/NCAR 40-Year Reanalysis Project , 1996, Renewable Energy.

[22]  Haomin Zhou,et al.  Adaptive Local Iterative Filtering for Signal Decomposition and Instantaneous Frequency analysis , 2014, 1411.6051.

[23]  Thomas Y. Hou,et al.  Adaptive Data Analysis via Sparse Time-Frequency Representation , 2011, Adv. Data Sci. Adapt. Anal..

[24]  Khaled H. Hamed,et al.  Time-frequency analysis , 2003 .

[25]  I. Daubechies,et al.  Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool , 2011 .

[26]  Antonio Cicone,et al.  Hyperspectral chemical plume detection algorithms based on multidimensional iterative filtering decomposition , 2015, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[27]  Dimitris G. Manolakis,et al.  Detection algorithms for hyperspectral imaging applications , 2002, IEEE Signal Process. Mag..

[28]  Jérôme Gilles,et al.  Empirical Wavelet Transform , 2013, IEEE Transactions on Signal Processing.