A simple M-dimensional model-based phase unwrapping based on integration by parts

In this paper, we propose a simple method for model based multidimensional phase unwrapping to estimate the multivariate polynomial phase from an observed complex signal. The main idea of the proposed method is a simple reduction of the original problem of multidimensional phase estimation to a system of linear equations based on the well known integration by parts. By this reduction, exhaustive numerical maximization techniques become unnecessary, unlike the conventional methods, and any linear inverse technique can be applied with additional, if necessary, a prior knowledge to suppress the effect of any perturbation due to the measurement noises or the numerical errors caused mainly by numerical integrations