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On the L0-Norm Based Sparse Time-Frequency Distribution Reconstruction

Joint time-frequency (TF) domain often provides an additional insight into the observed phenomenon, rather than observing the phenomenon in the time and frequency domain separately. Recently, a compressive sensing (CS) approach has been proposed to solve one of the main problems of the signal TF representation: the removal of artefacts. These artefacts, also called the cross-terms, are a mathematical byproduct of the time-frequency distribution (TFD) calculation, and are usually suppressed with a low-pass filtering, the procedure which also reduces the TF resolution. The resolution loss, in the CS based approach, is avoided by an optimization procedure, which enforces the sparsity constraints to the resulting sparse TFD. In this paper, we investigate the application of the 0-norm based reconstruction algorithms for the sparse TFD calculation. Furthermore, we employ the adaptive CS scheme in order to improve the quality of the resulting sparse TFDs, while reducing the reconstruction algorithm execution time.

Signal sparsity, Compressive sensing, Time-frequency distributions, Ambiguity function, l0-norm, Signal reconstruction.

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