Parameter Selection Criteria for Tomo-SAR Focusing

The synthetic aperture radar (SAR) tomography (TomoSAR) inverse problem is commonly tackled in the context of the direction-of-arrival estimation theory. The latter allows achieving super resolution, along with ambiguity levels reduction, thanks to the use of parametric focusing methods, as multiple signal classification (MUSIC) and statistical regularization techniques, like the maximum-likelihood-inspired adaptive robust iterative approach (MARIA). Nevertheless, in order to correctly suit the considered signal model, MUSIC and most regularization approaches require an appropriate setting of the involved parameters. In both cases, the accuracy of the retrieved solutions depends on the right selection of the assigned values. Thus, with the aim of dealing with such an issue, this article addresses several parameter selection strategies, adapted specifically to the TomoSAR scenario. Parametric techniques as MUSIC solve the TomoSAR problem in a different manner as the regularization methods do, hence, each approach demands different methodologies for the proper estimation of their parameters. Consequently, we refer to the Kullback-Leibler information criterion for the model order selection of parametric techniques as MUSIC, whereas we rather explore the Morozov's discrepancy principle, the L-Curve, the Stein's unbiased risk estimate, and the generalized cross-validation to choose the regularization parameters. After the incorporation of these criteria to MUSIC and MARIA, respectively, their capabilities are first analyzed through simulations, and later on, utilizing real data acquired from an urban area.