Maximum a Posteriori Inversion for Forest Height Estimation Using Spaceborne Polarimetric SAR Interferometry

The model-based inversion of spaceborne polarimetric interferometric synthetic aperture radar (PolInSAR) has great potential for large-scale forest height estimation. The inversion performance strongly depends on the accurate estimation of ground phase and volume coherence, and these aspects still need to be addressed due to the double-candidate effect of the ground phase. This article introduces a maximum a posteriori (MAP) inversion method based on the two-layer randomly oriented volume over ground model to achieve a more accurate forest height estimation. Firstly, the components of the interferometric phase from different polarizations are analyzed and formulated. Among them, the topographic phase is found to be equivalent to the ground phase when disregarding the vertical error of the external digital elevation model (DEM). Then, the ground phase is modeled as a Gaussian distribution based on the topographic phase and the external DEM. The MAP estimate of the ground phase is derived by combining the prior distribution of the ground phase and the complex Wishart distribution of the observed covariance matrix. Finally, the forest height is inverted according to the optimally recovered volume-only coherence. The proposed method is verified through spaceborne L-band repeat-pass SAOCOM acquisitions over the forest test site in Foresta di Acquafrida, Santa Giusta, Province of Oristano, Italy. The inversion performance is validated against light detection and ranging (LiDAR) data obtained from spaceborne ICESat-2 acquisitions. The results demonstrate that the proposed method reaches a mean error of 5.73 m and an root mean square error (RMSE) of 8.04 m to the pixel level, which improves 36.02% and 24.05% compared with the existing method, respectively.