Evaluating Phase Histograms for Remote Sensing of Forested Areas Using L-Band SAR: Theoretical Modeling and Experimental Results

This article evaluates the recently introduced phase histogram (PH) technique for estimating forest height and vertical structure using theoretical modeling and experimental synthetic aperture radar (SAR) data. The PH technique assigns each pixel in an SAR interferogram to a specific height bin based on the value of the corresponding interferometric phase, thus allowing for the estimation of the forest's vertical structure by accumulating pixels magnitudes within a given spatial window. This approach is radically different from the one employed by SAR tomography (TomoSAR), which allows for direct imaging of the 3-D structure of the vegetation by jointly focusing on SAR data from multiple trajectories. Importantly, PHs can be built using as few as two images (a single interferogram), whereas TomoSAR is well-known to perform best when many images area available. Accordingly, the main question we intend to address in this article is to what extent and in which conditions single-baseline PHs can be used as a surrogate of TomoSAR (in the absence of multibaseline data). Experimental analyses are conducted using L-band tomographic SAR data from the ESA campaign TomoSense, flown in 2020 at Eifel Park in North West Germany. TomoSense data include 30 + 30 monostatic overpasses acquired along two opposite flight headings, and are complemented by airborne, terrestrial, and unmanned aerial vehicle (UAV) Lidar surveys. Lidar data are used to generate a forest canopy height model (CHM) and vertical profiles of leaf area density (LAD), taken as the main reference in the evaluation of PHs. Multibaseline tomographic data are produced and investigated to assess the actual sensitivity of radar data to forest structure at this site, as well as to provide indications about the performance of a radar instrument when multiple baselines are available. Experimental results indicate that the PH technique can only loosely approximate the vertical structure produced by TomoSAR. Still, it can produce a reasonably good estimate of forest height. In particular, TomoSAR and the PH technique are observed to have an average root mean square error (RMSE) with respect to Lidar estimate of 2.8 and 4.45 m in North-West heading data, and 1.84 and 5.46 m in South-East heading data, respectively. The observed results are interpreted in light of a simple physical model to characterize PHs depending on the number of scatterers within the SAR resolution cell, on which basis we derive analytical expressions to predict height dispersion in PHs. The proposed model indicates that the concept of PH is inherently based on the assumption of a single dominant scatterer within any single SAR resolution cell. If this is not the case, PHs produce an intrinsic dispersion that does not represent the actual vertical distribution of scatterers within the vegetation. Consistently, we conclude that the PH technique is inherently best suited for the analysis of high- or very-high resolution data, which suggests its use in the context of higher frequency SAR missions (e.g., Tandem-X) and when there are few acquisitions available.