the atomic norm can be efficiently computed but suffers from a resolution limit as mentioned above. We propose a novel sparse metric and theoretically show that the new metric fills the gap between the atomic $\ell_0$ norm and the atomic norm. It approaches the former under appropriate parameter setting and breaks the resolution limit. Using this sparse metric we formulate a nonconvex optimization problem for signal and frequency recovery. A locally convergent iterative algorithm is presented to solve the problem. Some further analysis shows that the algorithm iteratively carries out ANM with a sound reweighting strategy that determines preference of frequency selection based on the latest estimate and enhances sparsity and resolution. The resulting algorithm is termed as reweighted atomic-norm minimization (RAM). Extensive numerical simulations are carried out to demonstrate the performance of RAM with application to DOA estimation compared to existing art.

We note that the idea of reweighted optimization for enhancing sparsity is not new. For example, reweighted $\ell_1$ algorithms have been introduced for discrete CS [@lobo2007portfolio; @candes2008enhancing; @wipf2010iterative; @stoica2014weighted], and reweighted trace minimization for low rank matrix recovery (LRMR) [@fazel2003log; @mohan2012iterative]. However, it is unclear how to implement a reweighting strategy in the continuous dictionary setting until 