Compressive sensing meets time-frequency: An overview of recent advances in time-frequency processing of sparse signals

Compressive sensing is a framework for acquiring sparse signals at sub-Nyquist rates. Once compressively acquired, many signals need to be processed using advanced techniques such as time-frequency representations. Hence, we overview recent advances dealing with time-frequency processing of sparse signals acquired using compressive sensing approaches. The paper is geared towards signal processing practitioners and we emphasize practical aspects of these algorithms. First, we briefly review the idea of compressive sensing. Second, we review two major approaches for compressive sensing in the time-frequency domain. Thirdly, compressive sensing based time-frequency representations are reviewed followed by descriptions of compressive sensing approaches based on the polynomial Fourier transform and the short-time Fourier transform. Lastly, we provide brief conclusions along with several future directions for this field.