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 (2-D) 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 and are derived for the parallel one-dimensional (1-D) problem. These criteria are then adapted to the 2-D problem using heuristic arguments. Employing asymptotic considerations, we derive a maximum a posteriori (MAP) model order selection criterion for jointly estimating the parameters of the 2-D sinusoids and their number. The proposed model order selection rule is strongly consistent. As an example, the model order selection criterion is applied as a component in an algorithm for parametric estimation and synthesis of textured images.