The Local Rényi Entropy Based Shrinkage Algorithm for Sparse TFD Reconstruction

Abstract

Observing a non-stationary signal with the time and frequency representation being mutually exclusive often does not provide enough information. Thus, the joint time-frequency distribution (TFD) is used as a convenient and powerful tool for analysis of such signals. Although TFD overcomes many signal representation limitations, it also introduces additional challenges. The removal of artefacts, also called the cross-terms, while maintaining a high concentration of the signal components (auto-terms) is the main problem of the time-frequency (TF) signal analysis. Among different approaches of solving this problem, in this paper we are investigating the advantages of the TFD sparsity, that is, the fact that the energy is accumulated around the instantaneous frequency law of the signal components. In this paper, we present a sparse TFD reconstruction algorithm based on the iterative shrinkage algorithm. The shrinkage is performed independently for each TFD time-and frequency-slice by taking advantage obtained from the short-term and the narrow-band Rényi entropy. Using the TFD concentration measure and reconstruction algorithm execution time, the obtained results have been compared to the state-of-the-art sparse reconstruction algorithms.