This paper is concerned with spectral estimation of a finite number of two dimensional sinusoids embedded in white noise. Closed form expressions are derived for estimates using the autoregressive (AR) prediction error filter approach, as well as using periodogram with Bartlett window, and the maximum likelihood (ML) method. These expressions are useful in the study of resolving closely spaced sinusoidal signals. Over a narrow frequency band, direct decimation can be applied to improve resolution and/or to reduce computation. simulation results demonstrate that decimation by (D1,D2) with a support size (N1,N2) yields approximately the same resolution as a support size (D1N1,D2N2) used with the undecimated signal. The use of decimation also reduces significantly computation.