  Existing approaches to compressive sensing of frequency-sparse signals
focuses on signal recovery rather than spectral estimation. Furthermore, the
recovery performance is limited by the coherence of the required sparsity
dictionaries and by the discretization of the frequency parameter space. In
this paper, we introduce a greedy recovery algorithm that leverages a
band-exclusion function and a polar interpolation function to address these two
issues in spectral compressive sensing. Our algorithm is geared towards line
spectral estimation from compressive measurements and outperforms most existing
approaches in fidelity and tolerance to noise.
