A Null-Space Method for the Phase Unwrapping of Multitemporal SAR Interferometric Stacks

Multitemporal differential interferometric synthetic aperture radar analysis is of fundamental importance in the monitoring of Earth surface displacements. In this context, a key role for the reconstruction of the deformation maps and time series is played by the phase unwrapping (PhU) that reconstructs the unrestricted phase signals starting from the measured wrapped versions, i.e., the interferograms. PhU is typically carried out independently for each interferogram in the 2-D azimuth-range domain via the efficient minimum cost flow (MCF) optimization technique. Recently, it has been proposed a two-step (TS) strategy that exploits both the temporal and the spatial structures of the available interferograms. The MCF algorithm is applied in this case also in the temporal/spatial baseline domain, and this step is combined with the classical 2-D space unwrapping. However, the restriction on the use of the MCF algorithm in the baseline domain poses limitations on the interferogram generation scheme. We present a formulation which makes use of the overdetermined nature of the operator that relates the phase differences to the absolute phase values: the problem is addressed in a more general framework that can cope with the 3-D (2-D space and time) nature of the data. This formulation is derived with reference to the sequential (TS) approach to overcome its restrictions on the interferogram generation. The new algorithm is validated on both simulated and real data. Moreover, the use of this new formulation for a full 3-D unwrapping is also addressed.