In this talk we present pieces from our work on sparsity-driven SAR imaging over the last 10 years or so. One of the earlier motivations for our work has been the increased interest in using SAR images in automated decision-making tasks such as automatic target recognition. The success of such tasks depends on how well the computed images exhibit certain features (e.g., scatterer locations, object boundaries) of the underlying scenes. Sparsity has turned out to be a useful asset for preserving and enhancing such features. We have developed both "analysis" and "synthesis" versions of a sparse signal representation-based approach for SAR imaging. The algorithms we have developed address a number of interesting challenges posed by the complex-valued nature of SAR imaging. The resulting images offer improvements over conventional images in terms of visual and automatic interpretation of the underlying scenes. Another motivation that has then driven our work has been the emergence of a number of applications in which the scene is observed through a sparse aperture. Examples include wide-angle imaging with unmanned air vehicles (UAVs), foliage penetration radar, bistatic imaging, and passive radar imaging. Sparsity-driven methods have turned out to be useful in sparse-aperture imaging scenarios as well. Of particular interest is a number of methods we have developed for wide-angle SAR imaging in the case of anisotropic scattering. We have also considered the problem of selection of parameters balancing sparsity and data fidelity objectives, and demonstrated the use of a number of automatic hyperparameter choice methods for SAR imaging. We have also considered the use of ideas and tools from compressed sensing to analyze SAR imaging from data exhibiting non-dense and irregular sampling patterns. Compressed sensing is primarily motivated by the fact that current radar sensing missions involve timeline constraints on data collection due to radar operation in multiple modes including searching, tracking, and imaging. We present an experimental study examining the implications of various mono-static and multi-static measurement configurations on SAR reconstruction performance. We have recently considered the problem of SAR imaging in the case of errors in the measurement model, due to, e.g., sensor platform position uncertainties. We have developed a sparsity-driven framework for joint SAR imaging and model error correction, leading to autofocusing. Finally, we describe ongoing work on an extension of this framework to the problem of moving target SAR imaging.
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