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Bayesian SAR imaging

We introduce a maximum a posteriori (MAP) algorithm and a sparse learning via iterative minimization (SLIM) algorithm to synthetic aperture radar (SAR) imaging. Both MAP and SLIM are sparse signal recovery algorithms with excellent sidelobe suppression and high resolution properties. The former cyclically maximizes the a posteriori probability density function for a given sparsity promoting prior, while the latter cyclically minimizes a regularized least squares cost function. We show how MAP and SLIM can be adapted to the SAR imaging application and used to enhance the image quality. We evaluate the performance of MAP and SLIM using the simulated complex-valued backscattered data from a backhoe vehicle. The numerical results show that both MAP and SLIM satisfactorily suppress the sidelobes and yield higher resolution than the conventional matched filter or delay-and-sum (DAS) approach. MAP and SLIM outperform the widely used compressive sampling matching pursuit (CoSaMP) algorithm, which requires the delicate choice of user parameters. Compared with the recently developed iterative adaptive approach (IAA), MAP and SLIM are computationally more efficient, especially with the help of fast Fourier transform (FFT). Also, the a posteriori distribution given by the algorithms provides us with a basis for the analysis of the statistical properties of the SAR image pixels.