A data driven compressive sensing approach for time-frequency signal enhancement

Signals with the time-varying frequency content are generally well represented in the joint time-frequency domain; however, the most commonly used methods for time-frequency distributions (TFDs) calculation generate unwanted artifacts, making the TFDs interpretation more difficult. This downside can be circumvented by compressive sensing (CS) of the signal ambiguity function (AF), followed by the TFD reconstruction based on the sparsity constraint. The most critical step in this approach is a proper CS-AF area selection, with the CS-AF size and shape being generally chosen experimentally, hence decreasing the overall reliability of the method. In this paper, we propose a method for an automatic data driven CS-AF area selection, which removes the need for the user input. The AF samples picked by the here-proposed algorithm ensure the optimal amount of data for the sparse TFD reconstruction, resulting in higher TFD concentration and faster sparse reconstruction algorithm convergence, as shown on examples of both synthetical and real-life signals.