Overlapping-Group-Lasso-Based ISAR Imagery via Alternating Direction Method of Multipliers

In this paper, we propose a novel method called overlapping group Lasso to solve inverse synthetic aperture radar (ISAR) imaging problem. Unlike the traditional least absolute shrinkage and selection operator (Lasso) model, overlapping group Lasso is based on the $\ell_{1}/\ell_{2}$ mixed-norm and take advantage of the prior knowledge of the continuity structures of the scatters. Besides, we present a generic optimization approach, the alternating direction method of multipliers (ADMM) method, for dealing with overlapping group Lasso that including structured-sparsity penalties and the predefined weight for group. ADMM is a simple but powerful algorithm that blending the benefits of augmented Lagrangian and dual decomposition method. Therefore, it makes the proposed algorithm faster and more robust. Experimental results of simulated data and Yak-42 real data verify the feasibility of ADMM achieves sparse and structural feature enhancement via the overlapping group Lasso. The comparison of the results of overlapping group Lasso and Lasso shows: the new developed model has the good ability of denoising and structural feature enhancement.