Time-frequency signature reconstruction from random observations using multiple measurement vectors

A new approach for sparse nonstationary signal reconstruction based on multiple windows is introduced. Signals which are localizable in the time-frequency (TF) domain give rise to sparsity in the same domain. When combined, sparse reconstructions, applied to randomly sampled data and corresponding to different selected windows, provide enhanced TF signature estimation. Among possible orthogonal windows, we consider those which characterize the eigen-decomposition of reduced-interference quadratic time-frequency distribution kernels. The highly overlapping TF support of the windows' full-data spectrograms inspires the use of the multiple measurement vectors, in lieu of individual windowed signal recovery. It is shown that the proposed approach outperforms other reconstruction methods when only a single window is applied and is superior to reduced interference time-frequency distributions of random observations.

[1]  Boualem Boashash,et al.  Time-Frequency Signal Analysis and Processing , 2002 .

[2]  M.G. Amin.  Spectral decomposition of time-frequency distribution kernels , 1994, IEEE Trans. Signal Process..

[3]  Moeness G. Amin,et al.  Minimum-variance time-frequency distribution kernels , 1995, IEEE Trans. Signal Process..

[4]  Patrick Flandrin,et al.  Time-Frequency Analysis and Applications [From the Guest Editors] , 2013, IEEE Signal Process. Mag..

[5]  Patrick Flandrin,et al.  Time-Frequency/Time-Scale Analysis , 1998 .

[6]  Yonina C. Eldar,et al.  Block-Sparse Signals: Uncertainty Relations and Efficient Recovery , 2009, IEEE Transactions on Signal Processing.

[7]  William J. Williams,et al.  Fast implementations of generalized discrete time-frequency distributions , 1994, IEEE Trans. Signal Process..

[8]  William J. Williams,et al.  Multitaper reduced interference distribution , 2000, Proceedings of the Tenth IEEE Workshop on Statistical Signal and Array Processing (Cat. No.00TH8496).

[9]  Braham Himed,et al.  Reduced interference time-frequency representations and sparse reconstruction of undersampled data , 2013, 21st European Signal Processing Conference (EUSIPCO 2013).

[10]  Yimin Zhang,et al.  Compressive sensing in nonstationary array processing using bilinear transforms , 2012, 2012 IEEE 7th Sensor Array and Multichannel Signal Processing Workshop (SAM).

[11]  Irena Orovic,et al.  Robust Time-Frequency Analysis Based on the L-Estimation and Compressive Sensing , 2013, IEEE Signal Processing Letters.

[12]  William J. Williams,et al.  Improved time-frequency representation of multicomponent signals using exponential kernels , 1989, IEEE Trans. Acoust. Speech Signal Process..

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

[14]  David L Donoho,et al.  Compressed sensing , 2006, IEEE Transactions on Information Theory.

[15]  R.G. Baraniuk,et al.  Distributed Compressed Sensing of Jointly Sparse Signals , 2005, Conference Record of the Thirty-Ninth Asilomar Conference onSignals, Systems and Computers, 2005..

[16]  Richard G. Baraniuk,et al.  Multiple window time-frequency analysis , 1996, Proceedings of Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96).

[17]  E.J. Candes,et al.  An Introduction To Compressive Sampling , 2008, IEEE Signal Processing Magazine.

[18]  William J. Williams,et al.  Reduced Interference Time-Frequency Distributions , 1992 .

[19]  Moeness Amin,et al.  Instantaneous frequency and time-frequency signature estimation using compressive sensing , 2013, Defense, Security, and Sensing.

[20]  James W. Pitton.  Time-frequency spectrum estimation: an adaptive multitaper method , 1998, Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis (Cat. No.98TH8380).

[21]  Patrick Flandrin,et al.  IEEE SIgnal Processing Magazine, Special issue on Time-Frequency Analysis and Applications , 2013 .

[22]  Patrick Flandrin,et al.  Time-Frequency Energy Distributions Meet Compressed Sensing , 2010, IEEE Transactions on Signal Processing.

[23]  Braham Himed,et al.  Complex multitask Bayesian compressive sensing , 2014, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[24]  Irena Orovic,et al.  Compressive Sensing Based Separation of Nonstationary and Stationary Signals Overlapping in Time-Frequency , 2013, IEEE Transactions on Signal Processing.

[25]  Maria Hansson.  Multiple Window Decomposition of Time-Frequency Kernels Using A Penalty Function for Suppressed Sidelobes , 2006, 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings.

[26]  S. Aviyente,et al.  Optimum window time-frequency distribution decompositions , 1998, Conference Record of Thirty-Second Asilomar Conference on Signals, Systems and Computers (Cat. No.98CH36284).

[27]  Patrick J. Loughlin,et al.  Multiple window non-linear time-varying spectral analysis , 1998, Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181).

[28]  David B. Dunson,et al.  Multitask Compressive Sensing , 2009, IEEE Transactions on Signal Processing.

[29]  Boualem Boashash,et al.  Multiple window spectrogram and time-frequency distributions , 1994, Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing.