frequency recovery. Section \[sec:RAM\] introduces the RAM algorithm. Section \[sec:implementation\] presents some algorithm implementation strategies for accuracy and speed considerations. Section \[sec:simulation\] provides extensive numerical simulations to demonstrate the performance of RAM. Section \[sec:conclusion\] concludes this paper.

Preliminary Gridless Sparse Methods by Exploiting Sparsity {#sec:preliminary}
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Unless otherwise stated, we assume in this paper that the observed data $\m{Y}_{\m{\Omega}}^o$ is contaminated by noise whose Frobenius norm is bounded by $\eta\geq0$. It is clear that $\eta=0$ refers to the noiseless case. The CCS problem is solved by exploiting sparsity in the sense that the number of frequency components $K$ is small. In particular, we seek a sparse candidate $\m{Y}$ that is composed of a few frequency components and is meanwhile consistent with the observed data by imposing that $\m{Y}\in\cS$, where Therefore, we first define a sparse metric of $\m{Y}$ and then optimize the metric over $\cS$ for its solution. The frequencies $\lbra{f_k}$ are estimated using the frequency components composing $\m{Y}$.

A direct sparse metric is the smallest number of frequency components composing $\m{Y}$, known as the atomic $\ell_0$ norm and denoted by $\norm{\m{Y}}_{\cA,0}$ [@tang2012compressed; @yang2014continuous; @yang2014exact]: where $\m{a}\sbra{f}=\mbra{1,e^{i2\pi f},\dots,e^{i2\pi\sbra{N-1}f}}^T\in\bC^N$ denotes a discrete sinusoid with frequency $f\in\bT$ and $\m{s}_k\in\bC^{L\times 1}$ is the 