Synthetic Aperture Radar Imaging using Basis Selection Compressed Sensing

A compressed sensing method with basis selection is applied to a millimeter-wave synthetic aperture radar (SAR) imaging system. With a large candidate set of bases to choose from and without any a priori knowledge of the proper basis, the proposed method selects the sparsifying basis during the first few iterations of the L1 optimization according to the information from incomplete measurements and the coherence between the measurement matrix and sparsifying matrices. Several decision metrics can be used to select the basis, including the impulsiveness and Gini index of the available image at the current iteration. The proposed method is tested on two examples: a simulated image and its SAR measurement, and an experimental measurement obtained at 150 GHz via roaster scanning. The results from the simulation and experiment indicate that the proposed algorithm can always find a very good basis from the set of over 270 bases within the first two to five iterations of the L1 optimization