MAP model order selection rule for 2-D sinusoids in white noise

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 white Gaussian noise field. Existing solutions to this problem are based on model order selection rules, derived for the parallel one-dimensional problem. These criteria are then adapted to the two-dimensional problem using heuristic arguments. Employing asymptotic considerations, we derive in this paper a maximum a-posteriori (MAP) model order selection criterion for jointly estimating the parameters of the two-dimensional sinusoids and their number.