The edgelist algorithm for constraining phase unwrapped solutions with additional geodetic information

Phase unwrapping as used in InSAR geodesy is the reconstruction of absolute phase from measured phase known only modulo 2 on a finite grid of points in either 2 two or three dimensions. Many effective methods have been developed for unwrapping SAR interferograms [1-5], however phase unwrapping is a key step in many other coherent imaging techniques as well. Network programming approaches [3-4] have so far proven to be the most effective of these. The minimum cost flow (MCF) phase unwrapping algorithm developed by Costantini [3], describes a global cost minimization problem involving flow between phase residues computed over closed loops. The recently developed " edgelist " algorithm [6-7], replaces the MCF formulation with its dual formulation where the closed loops are replaced by reliable edges as the basic construct. The edgelist formulation has several advantages over the original MCF formulation – it simplifies the representation of multi-dimensional phase unwrapping, it allows incorporation of data from external sources, like GPS, where available to better constrain the unwrapped solution, and it treats regularly sampled or sparsely sampled data alike. It thus is particularly applicable to time series InSAR where data are often irregularly spaced in time and individual interferograms can be corrupted with large decorrelated regions. Similar to the MCF network problem, our formulation also exhibits total unimodularity (TUM) which enables us to solve the integer program using efficient linear programming tools. The validity of the new formulation and the dual formulation approach has been verified by independent development of similar techniques by Costantini et al [8]. We have already illustrated the ability of this new unwrapping method to incorporate a priori information related to the geophysical phenomena and the area being studied, by applying it to a PS-InSAR dataset from the creeping section of the Central San Andreas Fault [6-7]. The biggest advantage of the edgelist formulation, however, is its ability to incorporate external geodetic measurements as constraints. The original MCF formulation is unable to