Synthetic Aperture Radar (SAR) Tomography is a technique to provide direct three-dimensional (3D) imaging of the illuminated targets by processing SAR data acquired from different trajectories. In a large part of the literature, 3D imaging is achieved by assuming mono-dimensional (1D) approaches derived from SAR Interferometry, where a vector of pixels from multiple SAR images is transformed into a new vector of pixels representing the vertical profile of scene reflectivity at a given range, azimuth location. However, mono-dimensional approaches are only suited for data acquired from very closely-spaced trajectories, resulting in coarse vertical resolution. In the case of continuous media, such as forests, snow, ice sheets and glaciers, achieving fine vertical resolution is only possible in the presence of largely-spaced trajectories, which involves significant complications concerning the formation of 3D images. The situation gets even more complicated in the presence of irregular trajectories with variable headings, for which the one theoretically exact approach consists of going back to raw SAR data to resolve the targets by 3D back-projection, resulting in a computational burden beyond the capabilities of standard computers. The first aim of this paper is to provide an exhaustive discussion of the conditions under which high-quality tomographic processing can be carried out by assuming a 1D, 2D, or 3D approach to image formation. The case of 3D processing is then further analyzed, and a new processing method is proposed to produce high-quality imaging while largely reducing the computational burden, and without having to process the original raw data. Furthermore, the new method is shown to be easily parallelized and implemented using GPU processing. The analysis is supported by results from numerical simulations as well as from real airborne data from the ESA campaign AlpTomoSAR.

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.

The European Space Agency (ESA) TomoSense campaign was designed to advance forest parameter retrieval in preparation for future spaceborne Synthetic Aperture Radar (SAR) missions. The campaign was flown in 2020-2021 at the Kermeter area in the Eifel Park, Germany, to acquire mono- and bi-static SAR data over a temperate forest in hilly topographic conditions. The data-set includes multi-baseline, full-polarimetric L-band airborne SAR data acquired in a bistatic configuration by flying two aricraft in close formation, to enable tomographic imaging of the vegetation. As largely discussed in the literature, achieving high quality tomographic imaging requires accurate compensation of any phase terms not directly associated with the scene geometry, which includes platform position errors in navigational data and, in the case of bistatic acquisitions, clock synchronization errors. Building on the distinct features of navigation and clock synchronization errors, this paper proposes a four-step calibration approach that progressively refines the data to achieve accurate tomographic imaging. In the first step, clock mismatches are retrieved and corrected based on a direct analysis of mono- and bi-static data acquired in the same flight. In the second step, single-pass time-varying baseline errors between platforms are iteratively inverted and corrected. The third step jointly analyses the data from all flights to fully restore the interferometric coherence in all interferograms. The last step produces the final trajectory correction by a bistatic implementation of the Phase Center Double Localization (PCDL) algorithm. Experimental results demonstrate that the proposed approach produces high quality tomographic imaging for both the mono- and the bi-static data-sets. Finally, we demonstrate the possibility of tomographic imaging by coherently combining the two data-sets.