A novel method based on the optimal normal matrix constraint and cross-iteration algorithm is proposed in this letter to estimate the forest height using the polarimetric interferometry synthetic aperture radar (PolInSAR) data. First, to avoid the null ground-to-volume ratio assumption of the three-stage method, we use the PolInSAR optimal normal matrix constraint method to find out the pure volume coherence. This method can also provide a more accurate initial value for the least-squares iteration. Second, the cross-iteration is used for the forest height inversion, which provides better selection of the best polarization channel and solves the ill-conditioned matrix in the traditional least-squares iteration algorithm. This new method is validated using the BioSAR 2008 P-band data. The results show that the proposed method achieves an average accuracy of 2.6 m, which is better than that of the three-stage inversion method [root-mean-square error (RMSE) = 5.89 m] and the 6-D nonlinear iteration method (RMSE = 4.42 m).

Due to the strong penetrability, long-wavelength synthetic aperture radar (SAR) can provide an opportunity to reconstruct the three-dimensional structure of the penetrable media. SAR tomography (TomoSAR) technology can resynthesize aperture perpendicular to the slant-range direction and then obtain the tomographic profile consisting of power distribution of different heights, providing a powerful technical tool for reconstructing the three-dimensional structure of the penetrable ground objects. As an emerging technology, it is different from the traditional interferometric SAR (InSAR) technology and has advantages in reconstructing the three-dimensional structure of the illuminated media. Over the past two decades, many TomoSAR methods have been proposed to improve the vertical resolution, aiming to distinguish the locations of different scatters in the unit pixel. In order to cope with the forest mission of European Space Agency (ESA) that is designed to provide P-band SAR measurements to determine the amount of biomass and carbon stored in forests, it is necessary to systematically evaluate the performance of forest height and underlying topography inversion using TomoSAR technology. In this paper, we adopt three typical algorithms, namely, Capon, Multiple Signal Classification (MUSIC), and Compressed Sensing (CS), to evaluate the performance in forest height and underlying topography inversion. The P-band airborne full-polarization (FP) SAR data of Lopè National Park in the AfriSAR campaign implemented by ESA in 2016 is adopted to verify the experiment. Furthermore, we explore the effects of different baseline designs and filter methods on the reconstruction of the tomographic profile. The results show that a better tomographic profile can be obtained by using Hamming window filter and Capon algorithm in uniform baseline distribution and a certain number of acquisitions. Compared with LiDAR results, the root-mean-square error (RMSE) of forest height and underlying topography obtained by Capon algorithm is 2.17 m and 1.58 m, which performs the best among the three algorithms.

This paper 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 a SAR interferogram to a specific height bin based on the value of the corresponding interferometric phase, thus allowing for the estimation of the forest 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 three-dimensional structure of the vegetation by jointly focusing SAR data from multiple trajectories. Importantly, phase histograms can be built using as few as two images (a single interferogram), whereas SAR tomography is well-known to perform best when many images area available. Accordingly, the main questions we intend to address in this paper is to what extent and in which conditions single-baseline phase histograms can be used as a surrogate of SAR tomography (in the absence of multi-baseline data). Experimental analyses are conducted using L-Band tomographic SAR data from the ESA campaign TomoSense, flown in 2020 at the 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 UAV (Unmanned Aerial Vehicle) 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 phase histograms. Multi-baseline 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 SAR tomography. 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 2.8m and 4.45m in North-West heading data, and 1.84m and 5.46m in South-East heading data, respectively. The observed results are interpreted in light of a simple physical model to characterize phase histograms depending on the number of scatterers within the SAR resolution cell, on which basis we derive analytical expressions to predict height dispersion in phase histograms. The proposed model indicates that the concept of phase histogram is inherently based on the assumption of a single dominant scatterer within any single SAR resolution cell. If this is not the case, phase histograms 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.

This paper compares two approaches for estimating forest height and vertical structure using synthetic aperture radar (SAR) data, namely the well-known SAR tomography (TomoSAR) technique and the recently introduced phase histogram (PH) technique. By jointly exploiting multiple SAR images, TomoSAR allows for direct imaging of the three-dimensional structure of the vegetation, from which biophysical parameters such as forest height and terrain topography can be extracted. The PH technique assigns each pixel in a SAR interferogram to a specific height bin based on the value of the corresponding interferometric phase, thus allowing for the estimation of the forest vertical structure by accumulating pixels magnitudes within a given spatial window. The two techniques are here compared on an experimental basis using L-Band tomographic data from the ESA campaign TomoSense, flown in 2020 at the Eifel Park in North West Germany. The analysis we present considers a characterization of forest scattering by 3D imaging and forest height retrieval. Experimental results indicate that the PH technique can only loosely approximate the vertical structure produced by SAR tomography. 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 2.63 m and 4.35 m in North-West heading data, and 1.84 m and 5.46 m in South-East heading data, respectively. The observed results are interpreted in light of a simple physical model to characterize phase histograms depending on the number of scatterers within the SAR resolution cell, on which basis we derive analytical expressions to predict height dispersion in phase histograms. The conclusion from both experimental and theoretical results is that phase histograms cannot correctly reproduce forest structure, unless the distribution of scatterers within the SAR resolution cell is characterized by a single dominant scatterer. 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.