is introduced as a convex relaxation of $\norm{\m{Y}}_{\cA,0}$ [@tang2012compressed; @yang2014continuous; @yang2014exact]: which is a continuous counterpart of the $\ell_{2,1}$ norm utilized for joint sparse recovery in discrete CS (see, e.g., [@malioutov2005sparse; @van2010theoretical]). $\atomn{\m{Y}}$ is a norm and has the following semidefinite formulation [@tang2012compressed; @yang2014continuous; @yang2014exact]: From the perspective of LRMR, (\[formu:AN\_SDP\]) attempts to recover the low rank matrix $T\sbra{\m{u}}$ by relaxing the pseudo rank norm in (\[formu:atom0norm\]) to the nuclear norm (or the trace norm for a PSD matrix). Again, the frequencies are encoded in $T\sbra{\m{u}}$ and can be obtained using the Vandermonde decomposition once the optimization problem is solved within a polynomial time. The atomic norm is computationally advantageous compared to the atomic $\ell_0$ norm while it suffers from a resolution limit due to the relaxation which is not shared by the latter [@candes2013towards; @tang2012compressed; @yang2014exact].

Enhancing Sparsity and Resolution via A Novel Sparse Metric {#sec:novelmetric}
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Inspired by the link between CCS and LRMR demonstrated above, we propose the following sparse metric of $\m{Y}$: where $\epsilon>0$ is a regularization parameter that avoids the first term being $-\infty$ when $T\sbra{\m{u}}$ is rank deficient. Note that the log-det heuristic $\log\abs{\cdot}$ has been widely used as a smooth surrogate for the 