A two-dimensional Prony's method for spectral estimation

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Abstract
In this paper 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. We propose to perform the estimation of frequencies, amplitudes, phases, and damping factors 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 factorizes in two parts so that many of their properties can be easily determined. In particular, our task is to find quick estimates of parameters computed by using standard one-dimensional autoregressive estimation methods. An iterative procedure for refining the autogressive parameters estimates is also discussed, which gives rise to better frequencies estimates. Some simulation results are reported

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