Combining multi-temporal SAR differential interferograms: A curvature based method

Given a series of SAR acquisitions, when a sufficient number of differential interferograms between different dates are computed and the phases unwrapped, the phases of each possible time interval can be obtained through a linear combination of the computed ones, i.e. by the solution of a determined linear system of equations. Usually (e.g. with ERS data), not all the interferograms necessary to obtain a determined system can be computed, unless one accepts that only few pixels (corresponding to stable point-like scatterers) remain coherent. In fact, spatial and temporal baselines can be very large. Previous works proposed to solve the under-determination of this system by singular value decomposition, i.e., by assuming that the solution (i.e. the terrain displacement) has minimum velocity. In this work, a different assumption is exploited in order to find a determined solution to the problem of combining SAR multi-temporal differential interferometric measurements. The proposed approach is based on the idea that the solution should have minimum curvature. Tests performed on simulated and ERS SAR real data confirm the validity of the method.