Sparse Recovery in Spaceborne SAR Tomography

Abstract

Synthetic aperture radar (SAR) tomography is a technique for reconstructing three-dimensional far field from two-dimensional measurements of radar echoes. As a result of a doctoral study, this dissertation addresses mainly several sparse recovery problems in spaceborne SAR tomography. Single-master SAR tomography uses a common acquisition for interferogram generation. In the single-look or single-snapshot case, each look or snapshot is processed independently. Under the assumption of a compressible far field in urban scenarios, this typically involves solving a complex-valued $\ell_1$-regularized least squares (L1RLS) problem. From a bi-criterion optimization point of view, each L1RLS solution associated with a fixed regularization parameter is Pareto optimal, and therefore its solution path can be sampled in order to achieve automatic tuning. Besides, we show empirically that a simple diagonal preconditioning can substantially improve the convergence of this notoriously ill-posed problem as applied to spaceborne SAR tomography. On the other hand, the far fields of various looks or snapshots are jointly reconstructed in the multi-look case. We show that the prior knowledge of scatterers sharing the same elevation position among different looks leads in general to a joint tensor mode recovery problem for repeat-pass acquisitions. Single-look multi-master SAR tomography is a relatively new research topic that is primarily inspired by prospective spaceborne SAR missions in bi- or multistatic configurations (i.e., with one transmitter and multiple receivers). We establish the single-look multi-master data model, and propose a generic inversion framework comprised of nonconvex sparse recovery, model-order selection and off-grid correction. Two algorithm are developed vis-à-vis nonconvex sparse recovery: one extends the conventional nonlinear least squares (NLS) to the single-look multi-master data model, and the other is based on bi-convex relaxation and alternating minimization. In addition, we prove two theorems regarding the critical points of the objective function of any NLS subproblem. We show empirically that the conventional single-look single-master approach, if applied to a single-look multi-master stack, can be insufficient for layover separation, even when the elevation distance between two scatterers is significantly larger than the Rayleigh resolution. In the end, we develop a hybrid approach for single-look pursuit monostatic acquisitions. This approach estimates first scatterers' elevation from solely pursuit monostatic interferograms, and subsequently their motion parameters from all acquisitions by exploiting the previous elevation estimates as deterministic prior. The former is a special case of single-look multi-master tomography, while the latter is a variant of single-look single-master tomography. This approach is directly applicable to bistatic acquisitions.