  We consider the problem of jointly estimating the number as well as the
parameters of two-dimensional sinusoidal signals, observed in the presence of
an additive colored noise field. We begin by elaborating on the least squares
estimation of 2-D sinusoidal signals, when the assumed number of sinusoids is
incorrect. In the case where the number of sinusoidal signals is
under-estimated we show the almost sure convergence of the least squares
estimates to the parameters of the dominant sinusoids. In the case where this
number is over-estimated, the estimated parameter vector obtained by the least
squares estimator contains a sub-vector that converges almost surely to the
correct parameters of the sinusoids. Based on these results, we prove the
strong consistency of a new model order selection rule.
