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31 May 2013 Compressive sensing for sparse time-frequency representation of nonstationary signals in the presence of impulsive noise
Irena Orović, Srdjan Stanković, Moeness Amin
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Abstract
A modified robust two-dimensional compressive sensing algorithm for reconstruction of sparse time-frequency representation (TFR) is proposed. The ambiguity function domain is assumed to be the domain of observations. The two-dimensional Fourier bases are used to linearly relate the observations to the sparse TFR, in lieu of the Wigner distribution. We assume that a set of available samples in the ambiguity domain is heavily corrupted by an impulsive type of noise. Consequently, the problem of sparse TFR reconstruction cannot be tackled using standard compressive sensing optimization algorithms. We introduce a two-dimensional L-statistics based modification into the transform domain representation. It provides suitable initial conditions that will produce efficient convergence of the reconstruction algorithm. This approach applies sorting and weighting operations to discard an expected amount of samples corrupted by noise. The remaining samples serve as observations used in sparse reconstruction of the time-frequency signal representation. The efficiency of the proposed approach is demonstrated on numerical examples that comprise both cases of monocomponent and multicomponent signals.
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Irena Orović, Srdjan Stanković, and Moeness Amin "Compressive sensing for sparse time-frequency representation of nonstationary signals in the presence of impulsive noise", Proc. SPIE 8717, Compressive Sensing II, 87170A (31 May 2013); https://doi.org/10.1117/12.2015916
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Cited by 21 scholarly publications.
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KEYWORDS
Time-frequency analysis

Compressed sensing

Reconstruction algorithms

Interference (communication)

Signal processing

Doppler effect

Modulation

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