Use of prior information and multiple interferograms in SAR phase unwrapping.

We extend the classical least-squares phase unwrapping algorithms to take advantage of available a~priori information and multiple acquisitions. In this inverse problem theory framework, we use several interferograms to build a single a~posteriori model, that represents a compromise between an initial model and phase uncertainties. This approach suppresses the overall uncertainty due to an ambiguous interferometric phase. With these improvements, Synthetic Aperture Radar (SAR) interferometry can be merged with exogenous data in a simple and robust fashion. In crustal deformation surveys, a~priori information may come from GPS data, radar amplitude images cross-correlation, or modeling. In topography applications, existing Digital Elevation Models (DEM) and sparse GPS data may also be combined to take advantage of both the relative accuracy of existing DEMs on large spatial scales, and the high resolution of SAR imagery. Prior model can also complement areas with low radar coherence, shadow and layover. Eventually, the expected model autocorrelation can be used as a regularization function to isolate wavelengths of interest depending on the application at hand. We illustrate these capabilities, first, performing a topography recovery from a stack of ERS interferograms acquired in the bay of Corinth (Greece). The SRTM DEM projected on the SAR geometry is used as a prior model and is noticeably improved by either stacking of interferograms or using a regularization. A comparison with a reference DEM and a set of GPS ground control points demonstrates altimetric refinements at the meter scale, even when unwrapping very noisy interferograms. Second, we show how a GPS/SPOT image correlation-based model can complement interferograms in incoherent areas with a set of differential interferograms imaging the 1999 Chi Chi, Taiwan earthquake.