Enhanced TomoSAR Imaging through Statistical Regularization

Synthetic aperture radar (SAR) tomography (TomoSAR) is a powerful remote sensing tool that allows the retrieval of a 3D representation of the illuminated scene [1] - [4]. A set of images, acquired with a different line-of-sight (LOS), is combined coherently using SAR interferometric techniques. Later on, the power spectrum pattern (PSP), in the direction perpendicular to the LOS (PLOS), is recovered using spectral analysis (SA)-based methods. The TomoSAR problem at hand is treated as an ill-conditioned nonlinear inverse problem [5], [6], and is commonly tackled within the direction-of-arrival (DOA) estimation framework [2] - [6]. The DOA-inspired non-parametric techniques, as the conventional matched spatial filter (MSF) and minimum variance distortionless response (MVDR) beamformers [1] - [4], are well suited to cope with distributed targets, since these techniques recover an estimate of the continuous power spectrum pattern (PSP); nonetheless, the achievable resolution highly depends on the span of the tomographic aperture. Alternatively, super-resolved parametric approaches, as multiple signal classification (MUSIC) [3], [4], have the main drawback related to the white noise model assumption that guaranties the separation of the signal and noise sub-spaces. On the other hand, taking advantage of the sparse representations of the cross-range tomographic profiles in the wavelet domain, super-resolved compressed sensing (CS)-based approaches [7], [8], are also employed to solve the TomoSAR inverse problem. However, CS-based techniques often imply a considerable computational burden, due to their iterative nature and due to the non-availability of adapted efficient convex optimization algorithms. To overcome such drawbacks and as an alternative to the aforementioned commonly performed TomoSAR-adapted focusing techniques, statistical regularization approaches can be applied instead, in the context of the statistical decision-making theory. Assuming no a priori knowledge about the statistical distribution of the desired PSP, to be retrieved, and imposing no constrain on linearity, the Bayes minimum risk (BMR) methodology is extended to the maximum-likelihood (ML) approach [5], [6]. Then, to guarantee well-conditioned solutions (in the Hadamard sense) to the TomoSAR nonlinear inverse problem, the derived ML-based approach is implemented in a closed fixed-point iterative adaptive manner, yielding the so-called MARIA (ML-inspired Adaptive Robust Iterative Approach) technique [5]. The use of statistical regularization approaches, within the maximum likelihood (ML) estimation theory, to solve the involved TomoSAR nonlinear ill-conditioned inverse problem, has been successfully demonstrated in the previous related studies [5], [6]. Within the main advantages of such approaches there is the retrieval of resolution-enhanced tomograms using a reduced (limited) number of passes, performing also suppression of artifacts and reduction of the ambiguity levels. Once the theoretical background of statistical regularization was provided, and its use for enhanced TomoSAR imaging was demonstrated, the subject of the work to be presented is focused on its application on different test sites and on the cross-check analysis of the retrieved measurements. [1] A. Reigber and A. Moreira, “First demonstration of airborne SAR tomography using multibaseline L-band data”, IEEE Trans. Geosc. Remote Sens., vol. 38, no. 5, pp. 2142–2152, Sep. 2000. [2] F. Gini, F. Lombardini and M. Montanari, “Layover solution in multibaseline SAR interferometry”, IEEE Trans. Aerosp. Electron. Syst., vol. 38, no.4, pp. 1344-1356, Oct. 2002. [3] M. Nannini, R. Scheiber, and A. Moreira, “Estimation of the minimum number of tracks for SAR tomography”, IEEE Trans. Geosc. Remote Sens., vol. 47, no. 2, pp. 531-543, Jan. 2009. [4] M. Nannini, R. Scheiber, R. Horn, and A. Moreira, “First 3-D reconstructions of targets hidden beneath foliage by means of polarimetric SAR tomography”, IEEE Geoscience and Remote Sensing Letters, vol. 9, no.1, pp. 60-64, Jan. 2012. [5] G. D. Martin del Campo, M. Nannini, and A. Reigber, “Towards Feature Enhanced SAR Tomography: A Maximum-Likelihood Inspired Approach”, IEEE Geoscience and Remote Sensing Letters, pp. 1–5, August 2018. [6] G. Martin del Campo, A. Reigber and M. Nannini, “Feature Enhanced SAR Tomography Reconstruction through Adaptive Nonparametric Array Processing”, IEEE International Geoscience and Remote Sensing Symposium (IGARSS), 2018. [7] E. Aguilera, M. Nannini and A. Reigber, “A Data-Adaptive Compressed Sensing Approach to Polarimetric SAR Tomography of Forested Areas”, IEEE Geoscience and Remote Sensing Letters, vol. 10, no.3, pp. 543–547, Sept. 2012. [8] E. Aguilera, M. Nannini and A. Reigber, “Wavelet-Based Compressed Sensing for SAR Tomography of Forested Areas”, IEEE Trans. Geosc. Remote Sens., vol. 51, no.12, pp. 5283–5295, Dec. 2013.