A CURVATURE BASED METHOD FOR COMBINING MULTI-TEMPORAL SAR DIFFERENTIAL INTERFEROMETRIC MEASUREMENTS

Considering multiple interferograms is a common practice in SAR differential interferometry. In fact, multitemporal SAR acquisitions are used for monitoring terrain displacements over a long period of time. Moreover, the use of multiple data sets can help reducing atmospheric artifacts in SAR interferometric measurements. Given a series of SAR acquisitions, when all the interferograms between consecutive dates are computed, consecutive differential phases (after phase unwrapping) can be simply summed to obtain the differential phases correspondent to all the possible time intervals (including the total one). More generally, to this goal it is not necessary that all the computed interferograms are time-consecutive, but it suffices that the differential 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. It is common in typical cases (e.g. with ERS data), that not all the interferograms necessary to the goal above can be computed, unless one accepts that only few pixels (corresponding to point-like scatterers) remain coherent. In fact, spatial and temporal baselines can be very large. So, an under-determined linear system of equations is in generally available. Previous works proposed to solve 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 real data confirm the validity of the method.