Enhanced Cohen class time-frequency methods based on a structure tensor analysis: Applications to ISAR processing

When dealing with time-frequency analysis, each distribution belonging to the Cohen class (CC) is defined by its kernel. It introduces a time-frequency smoothing which impacts on the time-frequency resolution and the cross-term disappearance. Depending on the application, the practitioner has to find the ''best'' compromise. In this paper, we suggest combining several CC time-frequency representations (TFRs), corresponding to coarse-to-fine scales of smoothing. Taking advantage of this diversity, our approach consists in differentiating the signal, assumed to be characterized by 2-D near-linear stable trajectories in the time-frequency plane, and the cross-terms, assumed to be geometrically unstructured. For this purpose, a ''confidence map'' for each TFR is deduced from a local variational analysis of the time-frequency distribution. The set of confidence maps is then used to combine the different TFRs in order to obtain an ''enhanced'' TFR. Our approach is compared with various conventional TFRs by using synthetic data. Despite a comparatively higher computational cost, the resulting enhanced TFR exhibits a high time-frequency resolution while having limited cross-terms. As simulation results confirm the effectiveness of our method, it is then applied in the field of inverse synthetic aperture radar (ISAR) processing.

[1]  Zheng Bao,et al.  Inverse synthetic aperture radar imaging of maneuvering targets based on chirplet decomposition , 1999 .

[2]  M. Lagunas-Hernandez,et al.  An improved maximum likelihood method for power spectral density estimation , 1984 .

[3]  J. Capon.  High-resolution frequency-wavenumber spectrum analysis , 1969 .

[4]  W. M. Carey,et al.  Digital spectral analysis: with applications , 1986 .

[5]  L. Cohen,et al.  Time-frequency distributions-a review , 1989, Proc. IEEE.

[6]  L. C. Trintinalia,et al.  Joint time-frequency ISAR using adaptive processing , 1997 .

[7]  J. Grajal,et al.  Atomic decomposition for ISAR imaging , 2006, 2006 IEEE Conference on Radar.

[8]  Jian Li,et al.  An adaptive filtering approach to spectral estimation and SAR imaging , 1996, IEEE Trans. Signal Process..

[9]  B. Russell,et al.  Selecting a fuzzy aggregation operator for multicriteria fault location problem , 2004, IEEE PES Power Systems Conference and Exposition, 2004..

[10]  Eric Grivel,et al.  Deterministic regression methods for unbiased estimation of time-varying autoregressive parameters from noisy observations , 2012, Signal Process..

[11]  Meryem Jabloun,et al.  Estimation of the instantaneous amplitude and frequency of non-stationary short-time signals , 2008, Signal Process..

[12]  Charles Soussen,et al.  Sparse multidimensional modal analysis using a multigrid dictionary refinement , 2012, EURASIP J. Adv. Signal Process..

[13]  Carl-Fredrik Westin,et al.  Representing Local Structure Using Tensors II , 2011, SCIA.

[14]  Stéphane Mallat,et al.  A Theory for Multiresolution Signal Decomposition: The Wavelet Representation , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[15]  Jian Li,et al.  IAA Spectral Estimation: Fast Implementation Using the Gohberg-Semencul Factorization , 2011, IEEE Trans. Signal Process..

[16]  K. Kodera,et al.  Analysis of time-varying signals with small BT values , 1978 .

[17]  Victor C. Chen.  Reconstruction of inverse synthetic aperture radar image using adaptive time-frequency wavelet transform , 1995, Defense, Security, and Sensing.

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

[19]  Petros Maragos,et al.  Time-frequency distributions for automatic speech recognition , 2001, IEEE Trans. Speech Audio Process..

[20]  Jian Li,et al.  Efficient mixed-spectrum estimation with applications to target feature extraction , 1995, Conference Record of The Twenty-Ninth Asilomar Conference on Signals, Systems and Computers.

[21]  Anna Scaglione,et al.  Product high-order ambiguity function for multicomponent polynomial-phase signal modeling , 1998, IEEE Trans. Signal Process..

[22]  Edward H. Adelson,et al.  The Design and Use of Steerable Filters , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[23]  George-Othon Glentis,et al.  Efficient Implementation of Iterative Adaptive Approach Spectral Estimation Techniques , 2011, IEEE Transactions on Signal Processing.

[24]  Jian Li,et al.  Efficient implementation of Capon and APES for spectral estimation , 1998 .

[25]  Thomas Kailath,et al.  ESPRIT-estimation of signal parameters via rotational invariance techniques , 1989, IEEE Trans. Acoust. Speech Signal Process..

[26]  Ronald R. Yager,et al.  Full reinforcement operators in aggregation techniques , 1998, IEEE Trans. Syst. Man Cybern. Part B.

[27]  Douglas L. Jones,et al.  An adaptive optimal-kernel time-frequency representation , 1995, IEEE Trans. Signal Process..

[28]  Shie Qian,et al.  Joint time-frequency transform for radar range-Doppler imaging , 1998 .

[29]  Yi-Hui Huang,et al.  Digital Sublime Photography , 2013 .

[30]  Ljubisa Stankovic,et al.  S-method in radar imaging , 2006, 2006 14th European Signal Processing Conference.

[31]  P. Kersten,et al.  Implementation of the Time-Frequency Distribution Series for SAR Applications , 2006, 2006 IEEE International Symposium on Geoscience and Remote Sensing.

[32]  Pierre Baylou,et al.  Estimating local multiple orientations , 2007, Signal Process..

[33]  Hernando Ombao,et al.  The SLEX Model of a Non-Stationary Random Process , 2002 .

[34]  G. Boultadakis,et al.  Time - frequency analysis of radar signals for ISAR applications , 2005, Proceedings of 2nd International Conference on Recent Advances in Space Technologies, 2005. RAST 2005..

[35]  R. O. Schmidt,et al.  Multiple emitter location and signal Parameter estimation , 1986 .

[36]  Stephane Kemkemian,et al.  Combining time-frequency transforms to create a sequence of instantaneous range-Doppler images in ISAR processing , 2011, Proceedings of 2011 IEEE CIE International Conference on Radar.

[37]  Yves Grenier,et al.  Time-dependent ARMA modeling of nonstationary signals , 1983 .

[38]  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.

[39]  Olivier Rioul,et al.  Time-scale energy distributions: a general class extending wavelet transforms , 1992, IEEE Trans. Signal Process..

[40]  Jun Yu Li,et al.  Time-varying complex spectral analysis via recursive APES , 1998 .

[41]  Erik G. Larsson,et al.  Efficient time-recursive implementation of matched filterbank spectral estimators , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[42]  Ki H. Chon,et al.  Time-varying properties of renal autoregulatory mechanisms , 2002, IEEE Transactions on Biomedical Engineering.

[43]  Til Aach,et al.  Analysis of Multiple Orientations , 2009, IEEE Transactions on Image Processing.

[44]  Jian Li,et al.  Source Localization and Sensing: A Nonparametric Iterative Adaptive Approach Based on Weighted Least Squares , 2010, IEEE Transactions on Aerospace and Electronic Systems.

[45]  Jian Li,et al.  RELAX-based estimation of damped sinusoidal signal parameters , 1997, Signal Process..

[46]  Shie Qian,et al.  Decomposition of the Wigner-Ville distribution and time-frequency distribution series , 1994, IEEE Trans. Signal Process..

[47]  Mengdao Xing,et al.  New ISAR imaging algorithm based on modified Wigner–Ville distribution , 2009 .

[48]  J. Bigun,et al.  Optimal Orientation Detection of Linear Symmetry , 1987, ICCV 1987.

[49]  George-Othon Glentis,et al.  Time-Recursive IAA Spectral Estimation , 2011, IEEE Signal Processing Letters.

[50]  Cornel Ioana,et al.  Time-Frequency Analysis Using Warped-Based High-Order Phase Modeling , 2005, EURASIP J. Adv. Signal Process..

[51]  Brian Litt,et al.  Time-frequency spectral estimation of multichannel EEG using the Auto-SLEX method , 2002, IEEE Transactions on Biomedical Engineering.

[52]  Erik G. Larsson,et al.  Fast Implementation of Two-Dimensional APES and CAPON Spectral Estimators , 2002, Multidimens. Syst. Signal Process..

[53]  Jacob Benesty,et al.  Recursive and Fast Recursive Capon Spectral Estimators , 2007, EURASIP J. Adv. Signal Process..

[54]  Salvador Gabarda,et al.  Detection of events in seismic time series by time-frequency methods , 2010 .

[55]  George-Othon Glentis,et al.  Efficient Algorithms for Adaptive Capon and APES Spectral Estimation , 2010, IEEE Transactions on Signal Processing.