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Description
SAR tomography (TomoSAR) is a powerful technique for characterizing natural volumes over large areas, as it enables three-dimensional mapping of reflectivity by coherently combining two-dimensional SAR images acquired along slightly shifted trajectories. SAR systems operating at low frequencies can be efficiently used in tomographic mode to characterize the vertical structure of densely forested environments. In practice, quantitative tomographic imaging is often achieved through non-parametric spectral analysis, but the resulting vertical resolution may be insufficient to precisely characterize forest structure. In such cases, parametric TomoSAR, which incorporates prior knowledge of the composition and shape of the vertical reflectivity profile of the imaged medium, provides a means of estimating relevant forest descriptors. Recent studies have shown that low-order models based on simple reflectivity templates can be effectively employed to accurately image forests at P-band.
Polarimetric diversity significantly enhances the capabilities of TomoSAR for three-dimensional characterization of complex scattering mechanisms, as well as for separating ground and volume contributions. This decomposition is usually performed using singular value decomposition (SVD), which expresses the covariance structure as a sum of two Kronecker products. Among the infinite number of possible solutions, a particular solution can then be selected to represent the polarimetric and tomographic responses of the ground and overlying volume. Despite being optimal in the least-squares sense, the SVD-based solution presents several limitations, including the lack of positive semi-definiteness (PSD) of the retrieved components, which may occur for a small number of samples, and a loss of separation performance when the vertical resolution is low. Applying parametric TomoSAR independently to each decomposition term is not fully satisfactory, as it neither improves the polarimetric characterization nor prevents leakage between the two components identified during the decomposition.
This paper proposes an alternative to SVD based on joint diagonalization using special unitary operators, followed by parametric TomoSAR focusing directly in the optimized polarimetric space. The main features of the proposed approach are:
- guaranteed estimation of PSD components, owing to the use of unitary transformations, regardless of the number of available samples;
- preservation of the mutual dependence between spatial and polarimetric estimates during the focusing process, by which different spatial solutions lead to different polarimetric features.
The validity of the proposed technique is demonstrated through selected examples, while its relevance and performance are quantitatively assessed using BIOMASS PolTomoSAR data acquired over tropical forests.