Topological Characterization and Advanced Noise-Filtering Techniques for Phase Unwrapping of Interferometric Data Stacks

This chapter addresses the problem of phase unwrapping interferometric data-stacks, obtained by multiple SAR acquisitions over the same area on the ground, with a twofold objective. Firstly, a rigorous gradient-based formulation for the multi-channel phase unwrapping (MCh-PhU) problem is systematically established, thus capturing the intrinsic topological character of the problem. The presented mathematical formulation is consistent with the theoretical foundation of the discrete Calculus. Then, within the considered theoretical framework, we formally describe an innovative procedure for the noise filtering of time-redundant multi-channel multi-look interferograms. The strategy underlying the adopted multi-channel noise filtering (MCh-NF) procedure arises from the key observation that multi-look interferograms are not fully time-consistent, due to multi-look operations independently applied on each single interferogram. Accordingly, the presented MCh-NF procedure suitably exploits the temporal mutual relationships of the interferograms. Finally, we present some experimental results on real data and show the effectiveness of our approach applied within the well-known Small Baseline Subset (SBAS) processing chain, thus finally retrieving the relevant Earth's surface deformation time-series for geospatial phenomena analysis and understanding.