Model based phase unwrapping of 2-D signals

A parametric model and a corresponding parameter estimation algorithm for unwrapping two-dimensional phase functions, are presented. The proposed algorithm performs global analysis of the observed signal. Since this analysis is based on parametric model tting, 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 rst step the algorithm ts a 2-D polynomial model to the observed phase. The estimated phase is then used as a reference information which directs the actual phase unwrapping process: The phase of each sample of the observed eld is unwrapped by increasing (decreasing) it by the multiple of 2 which is the nearest to the di erence 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 eld is segmented, and each segment is t with its own model. Once the phase model of the observed eld has been estimated we can repeat the model-based unwrapping procedure described earlier for the case of a single segment and a single model eld. This work was partially supported by the United States Army Research O ce under Contract DAAL03-91C-0022, sponsored by U.S. Army Communications Electronics Command, Center for Signals Warfare.