We consider the problem of estimating the harmonics of a noisy 2-D signal. The observed data is modeled as a 2-D sinusoidal signal, with either random or deterministic phases, plus additive Gaussian noise of unknown covariance. Our method utilizes recently defined higher-order statistics, referred to as "mixed-cumulants", which permit a formulation that is applicable to both the random and deterministic case. In particular, we first estimate the frequencies in each dimension using an overdetermined Yule-Walker "type" approach. Then, the 1-D frequencies are paired using a matching criterion. To support our theory, we examine the performance of the proposed method via simulations.