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Recent research in off-the-grid compressed sensing (CS) has demonstratedthat, under certain conditions, one can successfully recover a spectrallysparse signal from a few time-domain samples even though the dictionary iscontinuous. In particular, atomic norm minimization was proposed in\cite{tang2012csotg} to recover $1$-dimensional spectrally sparse signal.However, in spite of existing research efforts \cite{chi2013compressive}, itwas still an open problem how to formulate an equivalent positive semidefiniteprogram for atomic norm minimization in recovering signals with $d$-dimensional($d\geq 2$) off-the-grid frequencies. In this paper, we settle this problem byproposing equivalent semidefinite programming formulations of atomic normminimization to recover signals with $d$-dimensional ($d\geq 2$) off-the-gridfrequencies.

Precise Semidefinite Programming Formulation of Atomic Norm Minimization for Recovering d-Dimensional ($d\geq 2$) Off-the-Grid Frequencies