On Solving SAR Imaging Inverse Problems Using Non-Convex Regularisation with a Cauchy-based Penalty

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Abstract

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 optimisation of a cost function that includes a non-convex Cauchy-based penalty. The convergence of the overall cost function optimisation 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 $L_1$ norms, and to the generalised 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.
Original languageEnglish
Number of pages17
JournalarXiv
Publication statusUnpublished - 1 May 2020

Keywords

  • Non-convex regularisation
  • Convex optimisation
  • Cauchy proximal operator
  • Inverse problems
  • Denoising
  • Image reconstruction

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