A two-dimensional Prony's method for spectral estimation

The problem of estimating the parameters of a model for bidimensional data made up by a linear combination of damped two-dimensional sinusoids is considered. Frequencies, amplitudes, phases, and damping factors are estimated by applying a generalization of the monodimensional Prony's method to spatial data. This procedure finds the desired quantities after an autoregressive model fitting to the data, a polynomial rooting, and a least-squares problem solution. The autoregressive models involved have a particular nature that simplifies the analysis. In fact, their characteristic polynomial factors into two parts so that many of their properties can be easily determined. Quick estimates of the parameters computed are found by using standard one-dimensional autoregressive estimation methods. An iterative procedure for refining the autoregressive parameters estimates which gives rise to better frequency estimates is also discussed. Some simulation results are reported