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Recently, compressive sensing (CS) has been applied in synthetic aperture radar (SAR) imaging, which is increasingly in the focus of study and shows great potential. In CS-based SAR imaging, motion errors of the moving platform introduce inaccuracies in the observation model, which cause various degradations in the final images. To accomplish accurate motion compensation during CS-based SAR imaging, we propose a fast CS-based SAR imaging integrated with motion compensation method. First, CS-based imaging based on the utilization of inverse observation deduced from the inversion of conventional imaging procedures is applied, which is much more computational efficient than the exact observation model. Then, an improved inverse observation model integrated with motion compensation is derived. In the improved model, spatially variant azimuth phase errors are taken into consideration. Joint SAR imaging and motion compensation are formulated as a sparse recovery problem and solved in an iterative way, wherein each iteration both image formation and motion compensation are carried out. The processing of SAR data shows that the proposed method can obtain better focused images compared with the existing SAR imaging and motion compensation methods.

Fast Compressive Sensing-Based SAR Imaging Integrated With Motion Compensation