Compressive Synthetic Aperture Radar Imaging and Autofocusing by Augmented Lagrangian Methods

We consider the problem of synthetic aperture radar (SAR) image reconstruction from undersampled data in the presence of phase errors. We formulate the problem as one of estimating both the phase errors and the underlying image simultaneously through optimization. Within that optimization framework, we use a combination of priors that have proven useful in radar imaging, including strong sparse scattering in the image domain, as well as piecewise smoothness (i.e., gradient sparsity). To solve the resulting optimization problems, we propose an alternating direction method of multipliers (ADMM), an augmented Lagrangian method, for compressive SAR image reconstruction. We use simulated and real data at varying undersampling rates to study the performance of the proposed method and compare it against existing methods in terms of convergence speed and reconstruction quality. Our method provides significant improvements in terms of image reconstruction quality and computation speed, as well as phase error estimation performance.