Model based phase unwrapping of 2-D signals

A parametric model and a corresponding parameter estimation algorithm for unwrapping 2-D phase functions are presented. The proposed algorithm performs global analysis of the observed signal. Since this analysis is based on parametric model fitting the proposed phase unwrapping algorithm has low sensitivity to phase aliasing due to low sampling rates and noise as well as to local errors. In its first step the algorithm fits a 2-D polynomial model to the observed phase. The estimated phase is then used as a reference information that directs the actual phase unwrapping process: The phase of each sample of the observed field is unwrapped by increasing (decreasing) it by the multiple of 2π which is the nearest to the difference between the principle value of the phase and the estimated phase value at this coordinate. In practical applications the entire phase function cannot be approximated by a single 2-D polynomial model. Hence the observed field is segmented and each segment is fit with its own model. Once the phase model of the observed field has been estimated we can repeat the model-based unwrapping procedure described earlier for the case of a single segment and a single model field.