Synthetic aperture radar (SAR) imagery can provide useful information in a
multitude of applications, including climate change, environmental monitoring,
meteorology, high dimensional mapping, ship monitoring, or planetary
exploration. In this paper, we investigate solutions to a number of inverse
problems encountered in SAR imaging. We propose a convex proximal splitting
method for the optimization of a cost function that includes a non-convex
Cauchy-based penalty. The convergence of the overall cost function optimization
is ensured through careful selection of model parameters within a
forward-backward (FB) algorithm. The performance of the proposed penalty
function is evaluated by solving three standard SAR imaging inverse problems,
including super-resolution, image formation, and despeckling, as well as ship
wake detection for maritime applications. The proposed method is compared to
several methods employing classical penalty functions such as total variation
(TV) and L1 norms, and to the generalized minimax-concave (GMC) penalty.
We show that the proposed Cauchy-based penalty function leads to better image
reconstruction results when compared to the reference penalty functions for all
SAR imaging inverse problems in this paper.Comment: 18 pages, 7 figure