Compressed sensing based robust time-frequency representation for signals in heavy-tailed noise

A compressed sensing approach for robust time-frequency analysis of signals corrupted by strong heavy-tailed noise is proposed. When using traditional time-frequency distributions and the corresponding ambiguity functions, the strong and impulsive nature of the noise introduces spurious peaks and compromises the sparse time-frequency signal reconstruction. In order to provide accurate localization of the signal power and reduce false positives, compressed sensing is applied to the robust ambiguity function based on the L-estimation approach. This enhances the sparse time-frequency trajectories that correspond to the instantaneous frequencies of signal components. Simulation examples involving non-Gaussian noise and signals with different instantaneous frequency laws are provided to demonstrate the effectiveness of the proposed approach.

[1]  Moeness G. Amin,et al.  Compressed sensing technique for high-resolution radar imaging , 2008, SPIE Defense + Commercial Sensing.

[2]  Igor Djurovic,et al.  Robust L-estimation based forms of signal transforms and time-frequency representations , 2003, IEEE Trans. Signal Process..

[3]  J. Romberg.  Imaging via Compressive Sampling [Introduction to compressive sampling and recovery via convex programming] , 2008 .

[4]  Moeness G. Amin,et al.  Through-the-Wall Human Motion Indication Using Sparsity-Driven Change Detection , 2013, IEEE Transactions on Geoscience and Remote Sensing.

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

[6]  Ljubisa Stankovic,et al.  Auto-term representation by the reduced interference distributions: a procedure for kernel design , 1996, IEEE Trans. Signal Process..

[7]  Moeness G. Amin,et al.  High spectral resolution time-frequency distribution kernels , 1998, IEEE Trans. Signal Process..

[8]  Aswin C. Sankaranarayanan,et al.  Compressive Sensing , 2008, Computer Vision, A Reference Guide.

[9]  R.G. Baraniuk,et al.  Compressive Sensing [Lecture Notes] , 2007, IEEE Signal Processing Magazine.

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

[11]  Ali Cafer Gürbüz,et al.  A Compressive Sensing Data Acquisition and Imaging Method for Stepped Frequency GPRs , 2009, IEEE Transactions on Signal Processing.

[12]  Michael A. Saunders,et al.  Atomic Decomposition by Basis Pursuit , 1998, SIAM J. Sci. Comput..

[13]  Douglas L. Jones,et al.  Signal-dependent time-frequency analysis using a radially Gaussian kernel , 1993, Signal Process..

[14]  Deanna Needell,et al.  CoSaMP: Iterative signal recovery from incomplete and inaccurate samples , 2008, ArXiv.

[15]  LJubisa Stankovic,et al.  Robust Wigner distribution with application to the instantaneous frequency estimation , 2001, IEEE Trans. Signal Process..

[16]  J. Romberg,et al.  Imaging via Compressive Sampling , 2008, IEEE Signal Processing Magazine.

[17]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

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

[19]  J. Tropp,et al.  CoSaMP: Iterative signal recovery from incomplete and inaccurate samples , 2008, Commun. ACM.