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.