Recent research in off-the-grid compressed sensing (CS) has demonstrated
that, under certain conditions, one can successfully recover a spectrally
sparse signal from a few time-domain samples even though the dictionary is
continuous. 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}, it
was still an open problem how to formulate an equivalent positive semidefinite
program for atomic norm minimization in recovering signals with d-dimensional
(d≥2) off-the-grid frequencies. In this paper, we settle this problem by
proposing equivalent semidefinite programming formulations of atomic norm
minimization to recover signals with d-dimensional (d≥2) off-the-grid
frequencies.Comment: 4 pages, double-column,1 Figur