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31 May 2013Compressive sensing for sparse time-frequency representation of nonstationary signals in the presence of impulsive noise
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, 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