Gridless compressed sensing under shift-invariant sampling

Parameter estimation has applications in many fields of signal processing, such as spectral analysis or direction-of-arrival estimation. Subspace-based methods like root-MUSIC and ESPRIT provide high parameter resolution at low computational complexity by exploiting specific sampling structure, namely uniform linear sampling and shift-invariant sampling, respectively. On the other hand, compressed sensing has been shown to outperform subspace-based methods in difficult scenarios such as low number of measurement vectors, high noise power or correlated signals. While it is well known that uniform sampling admits gridless compressed sensing methods, e.g., based on atomic norm minimization, no such approaches are known for shift-invariant sampling. In this paper we present a novel approach for gridless compressed sensing under shift-invariant sampling. We show by numerical experiments that the proposed method outperforms ESPRIT in difficult scenarios.