Handling Phase in Sparse Reconstruction for SAR: Imaging, Autofocusing, and Moving Targets

We consider sparse image reconstruction methods for synthetic aperture radar (SAR) and discuss how issues related to the phase of the complex-valued SAR reflectivities and the phase of the observed SAR data emerge and are handled in a number of currently available methods. In particular, we consider analysis and synthesis models for sparsity-driven SAR imaging, and discuss how the optimization problems in both cases need to treat the magnitudes and the phases of the reflectivities separately. Then, we consider errors in the SAR observation model, due to, e.g., imperfect knowledge of the SAR sensing platform. Such errors lead to phase errors in the SAR data and cause defocusing of the formed imagery. We describe how joint imaging and phase error correction can be performed in a sparsity-driven imaging framework. Finally, we consider the problem of SAR imaging in the presence of moving targets in the scene, and describe how that leads to more complicated phase errors. We discuss how sparsity can be used to attack this problem as well. We present experimental results illustrating the behavior of the methods discussed.