Sparse time-frequency distribution reconstruction based on the 2D Rényi entropy shrinkage algorithm

Time-frequency distributions (TFD) provide a set of powerful tools for the non-stationary signal analysis. Although TFD overcomes signal representation limitations, the most commonly used TFDs generate unwanted artefacts, also called the cross-terms, which make the TFD application less feasible for noise-corrupted real-life signals. In this paper, we investigate the advantages of the TFD sparsity by using the compressive sensing based methods. We propose a sparse reconstruction algorithm which reconstructs a TFD from a small sub-set of samples taken from the signal ambiguity function. The proposed algorithm is based on the iterative shrinkage algorithm which performance and robustness have been improved by utilizing the short-term and narrow-band Rényi entropies. Furthermore, we have circumvented the limitations of global concentration measure by coupling it with the measure based on the local Rényi entropy. The introduced concentration measures have been used as objective functions in a multi-objective meta-heuristic optimization of the proposed algorithm parameters, resulting in high-resolution TFDs while avoiding disjunctions within signal components. The obtained results have been compared to the state-of-the-art sparse reconstruction algorithms, for both noisy synthetic and real-life signals. •TFD sparsity by using compressive sensing based methods has been investigated.•Sparse reconstruction has been augmented with the local Rényi entropy.•The algorithm parameters have been optimized using meta-heuristic optimization.•A TFD with a highly concentrated auto-terms has been achieved.