Compressive recovery of 2-D off-grid frequencies

Estimation of two-dimensional frequencies arises in many applications such as radar, inverse scattering, and wireless communications. In this paper, we consider retrieving continuous-valued two-dimensional frequencies in a mixture of r complex sinusoids from a random subset of its n regularly-spaced timedomain samples. We formulate an atomic norm minimization program that, with high probability, guarantees perfect recovery from O(r log r log n) samples under a mild frequency separation condition. We propose to solve the atomic norm minimization via semidefinite programming, and validate the proposed algorithm via numerical examples. Our work extends the framework proposed by Tang et. al. [1] for line spectrum estimation to multidimensional spectrum estimation.