Robust Estimation of the Vertical Structure of Forest with Coherence Tomography

Abstract

In the last decade, the accurate and reliable estimation of forest biomass has gained increasing attention within the SAR remote sensing community, given its crucial role in terrestrial carbon budget. First approaches for biomass estimation were based on the allometric relation between biomass and top canopy height; however, the performance of such estimation is limited in forest systems with strong density variations. Recently, experimental evidence has suggested the possibility to extend the height to biomass allometry bay considering the vertical biomass distribution function. Conventional SAR Tomography techniques have demonstrated the capability of imaging the vertical structure by exploiting the spatial (i.e. baseline) diversity of the acquisitions, possibly jointly with polarization diversity. However, especially considering the implementation of space-borne missions, temporal decorrelation problems limit the number of suitable acquisition for the tomographic processing. For this reason, the Coherence Tomography (CT) technique has been recently proposed. In brief, CT aims at decomposing the vertical profile on a set of orthogonal basis functions through a least squares (LS) fitting with the available complex coherences (possibly obtained by combining different polarizations), after compensating them for the phase histories produced by the ground topography and the volume depth along the baselines. So doing, the tomographic reconstruction reduces to the estimation of the coefficients of the series and can be carried out with a low number of acquisitions. However, if the topography and the volume depth are not known or estimated with enough accuracy, the related phase errors dramatically affect the CT inversion, with misleading results in terms of vertical profiles. The same effect shows up also in presence of phase non-idealities due to atmospheric propagation and inaccuracies in the relative radar platform position measurements between the acquisitions. This work tackles the problem of the robust estimation of forest vertical profiles by means of CT in presence of the above mentioned phase errors. To counteract their effects, the proposed solution consists in relying as much as possible on the coherence amplitudes. It can be demonstrated that with the coherence amplitudes the reliable LS estimation is possible of the absolute values of the basis coefficients; to estimate their signs, the coherence phases can be used. This two-step CT is expected to furnish more accurate results with respect to the original CT inversion at the complex level. To increase the robustness, a constraint can be added to the LS estimation by exploiting the orthogonality of the basis functions. The performance in profile estimation of the proposed algorithm will be analyzed in controlled conditions by means of simulated coherences, with reference to realistic vertical profiles, and pros and cons discussed. In addition, first-cut real data results will be shown by using SAR data acquired with the DLR’s E-SAR airborne sensor.