Identification of phase unwrapping errors through the extension of the temporal coherence factor for redundant sequences of small baseline DInSAR interferograms

Advanced DInSAR techniques are used to investigate the temporal evolution of the deformations through the retrieval of the displacement time series, achieved through the inversion of an appropriate set of multi-temporal interferograms. Among them, the Small BAseline Subset (SBAS) is a well-established approach which has been widely used for the analysis of several deformation phenomena.

In this context, an effective and robust Phase Unwrapping (PhU) algorithm must be typically implemented and exploited in order to accurately retrieve the ground deformation signals. This operation represents a critical step because of the intrinsically ill-posed nature of the problem which may lead to solutions that, despite being mathematically correct, do not reproduce the actual unwrapped phase profile.

A common indicator for the quality of the PhU solution within advanced DInSAR methods like SBAS is the temporal coherence. This is a point-like parameter available for methods where the displacement time-series are retrieved through the inversion of an overdetermined linear equation system [M, N], with M>N, where M is the number of the generated (redundant) interferograms and N represents the exploited SAR images, whose solution can be obtained in the LS sense.

We present in the following a simple solution to identify and correct possible PhU errors, based on a different and innovative use of the temporal coherence parameter.

In principle, the higher the value of the temporal coherence, the better the quality of the PhU solution; however, unfortunately, the temporal coherence sensitivity decreases when the number of interferograms increases. To overcome this issue we propose to compute for each point a time series of local temporal coherences, computed by exploiting a limited number of interferograms. To do this, starting from the first acquisition date of the analysed dataset, we define a time window range, say Δw, and a time sampling, say t_i , where the step size Δt= t_i+1 -t_i  is selected in agreement with the satellite revisiting time. Accordingly, for the generic i-th step, we consider the time window centred around the t_i value and we calculate the temporal coherence by on a limited subset of interferograms whose master and/or slave images are included in the selected time window [t_i-Δw/2 , t_i+Δw/2]

This solution is computationally efficient and allows us to regain sensitivity on possible PhU errors. Indeed, by doing so, the number of interferograms to be analysed in order to identify those characterized by PhU errors has been drastically reduced, making the local temporal coherence more sensitive to small variations in a single interferogram. A subsequent algorithm of PhU errors correction can be then applied only to the involved interferograms, reducing the time computing and increasing the ability to spot and correct the wrong interferogram.