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, ob‐ tained by multiple SAR acquisitions over the same area on the ground, with a twofold objective. First, a rigorous gradient-based formulation for the multichannel phase un‐ wrapping (MCh-PhU) problem is systematically established, thus capturing the intrinsic topological character of the problem. The presented mathematical formulation is consis‐ tent with the theoretical foundation of the discrete calculus. Then within the considered theoretical framework, we formally describe an innovative procedure for the noise filter‐ ing of time-redundant multichannel multilook interferograms. The strategy underlying the adopted multichannel noise filtering (MCh-NF) procedure arises from the key obser‐ vation that multilook interferograms are not fully time consistent due to multilook opera‐ tions independently applied on each single interferogram. Accordingly, the presented MCh-NF procedure suitably exploits the temporal mutual relationships of the interfero‐ grams. Finally, we present some experimental results on real data and show the effective‐ ness of our approach applied within the well-known small baseline subset (SBAS) processing chain, thus finally retrieving the relevant Earth’s surface deformation time ser‐ ies for geospatial phenomena analysis and understanding.