even worse in the compressive data case. Capon’s beamforming and MUSIC are *high resolution* methods in the sense that they can break the aforementioned resolution limit. Since they are covariance-based methods sufficient snapshots are required to estimate the data covariance. Moreover, they are sensitive to source correlations. With the development of sparse signal representation and later the CS concept, sparse methods have been popular in the last decade which exploit the prior knowledge that the number of frequency components $K$ is small [@malioutov2005sparse; @hyder2010direction; @stoica2011new; @stoica2011spice; @wei2012doa; @fannjiang2012coherence; @hu2013doa; @duarte2013spectral; @liu2013sparsity; @hu2012compressed; @yang2012robustly; @yang2013off; @hu2013fast; @austin2013dynamic; @tan2014joint]. In these methods, however, the frequency domain $\bT$ has to be gridded/discretized into a finite set, resulting in the grid mismatch problem that limits the estimation accuracy as well as brings challenges to the theoretical performance analysis [@chi2011sensitivity; @yang2013off]. Though modified, off-grid estimation methods [@hu2012compressed; @yang2012robustly; @yang2013off; @hu2013fast; @austin2013dynamic; @tan2014joint] have been implemented to alleviate these drawbacks, overall they are still based on gridding of the frequency domain.

A mathematical theory of super-resolution was recently introduced by Candès and Fernandes-Granda [@candes2013towards]. They studied frequency estimation in the SMV, full data case and proposed a *gridless* convex optimization method based on the atomic norm 