Abstract—Sparse signal representations and approximations from overcomplete dictionaries have become an invaluable tool recently. In this paper, we develop a new, heuristic, graph-structured, sparse signal representation algorithm for overcomplete dictionaries that can be decomposed into subdictionaries and whose dictionary elements can be arranged in a hierarchy. Around this algorithm, we construct a methodology for advanced image formation in wide-angle synthetic aperture radar (SAR), defining an approach for joint anisotropy characterization and image formation. Additionally, we develop a coordinate descent method for jointly optimizing a parameterized dictionary and recovering a sparse representation using that dictionary. The motivation is to characterize a phenomenon in wide-angle SAR that has not been given much attention before: migratory scattering centers, i.e., scatterers whose apparent spatial location depends on aspect angle. Finally, we address the topic of recovering solutions that are sparse in more than one objective domain by introducing a suitable sparsifying cost function. We encode geometric objectives into SAR image formation through sparsity in two domains, including the normal parameter space of the Hough transform. Index Terms—Hough transforms, inverse problems, optimization methods, overcomplete dictionaries, sparse signal representations, synthetic aperture radar, tree searching. I.

Imagery formed from wide-angle synthetic aperture radar (SAR) measurements has fine cross-range resolution in principle. However, conventional SAR image formation techniques assume isotropic scattering, which is not valid with wide-angle apertures. Also, the spatial location of scattering centers may migrate as a function of viewing angle across the aperture. The problem of jointly forming images and characterizing anisotropy as well as characterizing scattering center migration in wide-angle SAR is considered in the thesis. The approach not only compensates for anisotropy and

In this paper, we introduce a new synthetic aperture radar (SAR) imaging modality which can provide a high-resolution map of the spatial distribution of targets and terrain using a significantly reduced number of needed transmitted and/or received electromagnetic waveforms. This new imaging scheme, requires no new hardware components and allows the aperture to be compressed. It also presents many new applications and advantages which include strong resistance to countermesasures and interception, imaging much wider swaths and reduced on-board storage requirements.