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This paper presents a new scheme called twodimensional mixed compressive sensing back-projection (CS-BP-2D), for synthetic aperture radar imaging on a geocoded grid, in a single measurement vector frame. The back-projection linear operator is derived in matrix form and a patched-based approach is proposed for reducing the dimensions of the dictionary. Spatial compressibility of the radar image is exploited by constructing the sparsity basis using the back-projection focusing framework and fast solving the reconstruction problem through the orthogonal matching pursuit algorithm. An artifact reduction filter inspired by the synthetic point spread function is used in post-processing. The results are validated for simulated and real-world SAR data. Sentinel-1 C-band raw data in both monostatic and spaceborne transmitter / stationary receiver bistatic configurations are tested. We show that CS-BP-2D can focus both monostatic and bistatic SAR images, using fewer measurements than the classical approach while preserving the amplitude, the phase, and the position of the targets. Furthermore, the SAR image quality is enhanced and also the storage burden is reduced by storing only the recovered complex-valued points and their corresponding locations.

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