Unwrapping ground displacement signals in satellite radar interferograms with aid of GPS data and MRF regularization

Synthetic aperture radar (SAR) images acquired by radar satellites at different times can be combined into interferograms that reveal information about the change in range from ground to satellite, wrapped into phase fringes corresponding to half the radar wavelength. We describe a methodology that uses Markov random field (MRF) regularization and simulated annealing optimization to unwrap such differential interferograms. Often, repeated global positioning system (GPS) geodetic measurements are available in an area covered by interferograms. Here, such repeated GPS observations are used to provide a complementary measurement of the unwrapped change in range at sparse locations. The process of unwrapping interferograms can be initialized and guided with such sparsely located "correct" values. Both interferograms and GPS observations may include several error factors, which are reduced before combining the two observations. GPS-measured range change is used to eliminate residual orbital error. In the unwrapping procedure, a vectorized lowpass filter is used to gain temporarily increased smoother variation of the phase. For the purposes of initializing the unwrapping process, virtual unwrapped interferograms are created by ordinary kriging of GPS-measured range change. The initial interferograms are then optimized further by using MRF regularization that incorporate the assumption of a smoothly varying displacement field and the relationship of the unwrapped images to the GPS observations. A simulated annealing optimization algorithm is used to find an optimal solution of the MRF regularization. The smoothed unwrapped interferograms are then used to construct unwrapped versions of the unfiltered input interferograms. Several additional image analyses methods are used in the optimization process to make the unwrapping more efficient and faster. The unwrapping technique is applied to unwrap interferograms from the Reykjanes Peninsula, in southwest Iceland.