The polynomial phase differencing algorithm for 2-D phase unwrapping: performance analysis

Abstract

We consider non-homogeneous 2-D signals which can be represented by a constant modulus polynomial-phase model. In previous papers we developed a computationally efficient estimation algorithm for the parameters of this model, and a novel phase unwrapping method which is based on this estimation algorithm. In this paper we analyze the performance of the algorithm and derive expressions for the mean squared error of the estimated coefficients. Assuming high signal to noise ratio (SNR), we show that the estimates are unbiased, and derive a rule for optimal selection of the algorithm parameters. The theoretical results are verified by Monte-Carlo simulations for selected examples. Finally, we present an approximate error analysis of the estimates for an arbitrary SNR. This analysis is carried out for a specific set of the algorithm parameters, which is selected based on the high SNR analysis.