CONICET | Buscador de Institutos y Recursos Humanos

We present a new space-time Phase Unwrapping (PhU) algorithm allowing us to analyze sequences of multitemporal full resolution differential Synthetic Aperture Radar (SAR) interferograms for the generation of surface deformation timeseries. The core of the proposed technique is represented by the Extended Minimum Cost Flow (EMCF) PhU algorithm [1] which was originally developed for analyzing sequences of multi-look interferograms. In particular, our method performs a joint analysis of the spatial and temporal relationships among a set of multi-temporal differential interferograms, compatible with the Small BAseline Subset (SBAS) algorithm [2]. It exploits the SAR data representation in the Temporal/Perpendicular baseline plane, where a Delaunay triangulation is computed. Each arc of this triangulation allows us to identify a SAR data pair to be exploited in the interferogram generation. Unfortunately, this approach may also lead to generate interferograms with large temporal and/or spatial baselines, which may be drastically corrupted by decorrelation phenomena. Accordingly, to avoid these effects, we also impose constraints on the maximum allowed interferogram baseline values, and we discard from the triangulation all the triangles that involve at least one ?large baseline? interferogram. Equivalently, we also remove triangles which involve SAR data pairs characterized by doppler centroid differences exceeding a selected threshold. The proposed PhU approach allows us to apply the SBAS inversion to the unwrapped full resolution differential synthetic aperture radar interferometry (DInSAR) phase sequences, with no need to pass through the analysis of the corresponding sequences of multi-look DInSAR interferograms [3]. On the other hand, the straightforward application of the MCF and EMCF techniques to unwrap sequences of full resolution interferograms is unfortunately often not feasible due to the large amount of ?phase residues? [4] to be compensated, which often leads to high-computing time or even unfeasible solutions of the network flow problems [4]. To properly cast this PhU problem, we suggest to use an effective divide-and-conquer approach to the spacetime phase unwrapping problem. The key idea is to split our complex minimum cost flow network problem, implementing the whole PhU step, into that of simplex sub-networks, which are solved by applying the EMCF approach. More precisely, we start by identifying, and solving, a primary network that involves a properly selected set of coherent pixels of our interferograms, which are characterized by phase signals with very limited spatial high-pass components. The results of this primary network minimization, representing the backbone structure of the overall network, are subsequently used to constrain the solution of the remaining sub-networks, including the whole set of coherent pixels. These PhU sub-networks are built relying on the generation of aConstrained Delaunay Triangulation (CDT) [5], whose constrained edges are relevant to the set of successfully unwrapped pixels analyzed during the first PhU operation. To clarify this issue, let us provide some basic information about CDT, which is a triangulation of a given set of vertices with the following properties: 1) a pre-specified set of non-crossing edges (referred to as constraints, or constrained edges) is included in the triangulation, and (2) the triangulation is as close as possible to a Delaunay one. The experimental results were achieved by applying the proposed approach to a dataset consisting of European Remote Sensing (ERS) SAR data acquired, from June 1992 to August 2007, over the Napoli (Italy) bay area. As a final remark, we want to stress that the availability of precise and computationally efficient PhU tools, when dealing with data processed at the full spatial resolution scale, may be very relevant for the future development of innovative interferometric processing techniques. For instance, the knowledge of the phase information associated to the set of successfully unwrapped points, as retrieved via the propose PhU technique at the full spatial resolution scale, may be exploited to perform ?enhanced? multilook operations.

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