Joint image formation and anisotropy characterization in wide-angle SAR

We consider the problem of jointly forming images and characterizing anisotropy from wide-angle synthetic aperture radar (SAR) measurements. Conventional SAR image formation techniques assume isotropic scattering, which is not valid with wide-angle apertures. We present a method based on a sparse representation of aspect-dependent scattering with an overcomplete basis composed of basis vectors with varying levels of angular persistence. Solved as an inverse problem, the result is a complex-valued, aspect-dependent response for each spatial location in a scene. Our non-parametric approach does not suffer from reduced cross-range resolution inherent in subaperture methods and considers all point scatterers in a scene jointly. The choice of the overcomplete basis set incorporates prior knowledge of aspect-dependent scattering, but the method is flexible enough to admit solutions that may not match a family of parametric functions. We enforce sparsity through regularization based on the ℓk-norm, k < 1. This formulation leads to an optimization problem that is solved through a robust quasi-Newton method. We also develop a graph-structured interpretation of the overcomplete basis leading towards approximate algorithms using guided depth-first search with appropriate stopping conditions and search heuristics. We present experimental results on synthetic scenes and the backhoe public release dataset.