A Case Study on the Correction of Atmospheric Phases for SAR Tomography in Mountainous Regions

Synthetic aperture radar (SAR) tomography with repeat-pass acquisitions generally requires a priori phase calibration of the interferometric data stack by compensating for the atmosphere-induced phase delay variations. These variations act as a disturbance in tomographic focusing. In mountainous regions, the mitigation of these disturbances is particularly challenging due to strong spatial variations of the local atmospheric conditions and propagation paths through the troposphere. In this paper, we assess a data-driven approach to estimate these phase variations under a regression-kriging framework. The vertical stratification of the troposphere is modeled functionally, while the impact of the spatial turbulence is considered in a stochastic sense. The methodology entails an initial persistent scatterer interferometry (PSI) analysis. The atmospheric phases isolated for the persistent scatterers (PS) within the PSI processing are considered as samples of the 3-D distribution of the phase delay variations over the scene. These atmospheric phases are regressed against the spatial coordinates in map geometry at PS locations. In turn, kriging predictions are obtained at each location along the elevation profile, where tomographic focusing is intended. A key point of this approach is that the requisite atmospheric corrections are incorporated within the tomographic focusing model. A case study has been performed on a data stack comprising 32 COSMO-SkyMed stripmap images acquired over the Matter Valley in the Swiss Alps, in the summers of 2008-2013. The results show locally improved deformation sampling with tomographic methods compared to the initial PSI solution, primarily due to the improved phase calibration. In general, this paper underscores the indispensability of height-dependent correction of atmospheric phases for SAR tomography.