Joint sparsity and frequency estimation for spectral compressive sensing

Parameter estimation from compressively sensed signals has recently received some attention. We here also consider this problem in the context of frequency sparse signals which are encountered in many application. Existing methods perform the estimation using finite dictionaries or incorporate various interpolation techniques to estimate the continuous frequency parameters. In this paper, we show that solving the problem in a probabilistic framework instead produces an asymptotically efficient estimator which outperforms existing methods in terms of estimation accuracy while still having a low computational complexity. Moreover, the proposed algorithm is also able to make inference about the sparsity level of the measured signal. The simulation code is available online.