An Augmented Lagrangian Method for autofocused Compressed SAR Imaging

We present an autofocus algorithm for Compressed SAR Imaging. The technique estimates and corrects for 1-D phase errors in the phase history domain, based on prior knowledge that the reflectivity field is sparse, as in the case of strong scatterers against a weakly-scattering background. The algorithm relies on the Sparsity Driven Autofocus (SDA) method and Augmented Lagrangian Methods (ALM), particularly Alternating Directions Method of Multipliers (ADMM). In particular, we propose an ADMM-based algorithm that we call Autofocusing Iteratively Re-Weighted Augmented Lagrangian Method (AIRWALM) to solve a constrained formulation of the sparsity driven autofocus problem with an ℓ_p-norm, p ≤ 1 cost function. We then compare the performance of the proposed algorithm´s performance to Phase Gradient Autofocus (PGA) and SDA [2] in terms of autofocusing capability, phase error correction, and computation time.