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

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 citetang2012csotg to recover 1-dimensional spectrally sparse signal. However, in spite of existing research efforts citechi2013compressive, 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.