# Ship Wake Detection in SAR Images via Sparse Regularization

## TL;DR

This paper introduces a novel sparse regularization method for detecting ship wakes in SAR images, outperforming existing techniques with an 80% success rate by formulating the problem as a convex inverse problem with a GMC penalty.

## Contribution

It proposes a new inverse problem approach using GMC regularization for ship wake detection in SAR images, demonstrating superior performance over state-of-the-art methods.

## Key findings

- GMC regularization achieves the best detection results.
- The proposed method outperforms existing approaches.
- 80% success rate in diverse SAR images.

## Abstract

In order to analyse synthetic aperture radar (SAR) images of the sea surface, ship wake detection is essential for extracting information on the wake generating vessels. One possibility is to assume a linear model for wakes, in which case detection approaches are based on transforms such as Radon and Hough. These express the bright (dark) lines as peak (trough) points in the transform domain. In this paper, ship wake detection is posed as an inverse problem, which the associated cost function including a sparsity enforcing penalty, i.e. the generalized minimax concave (GMC) function. Despite being a non-convex regularizer, the GMC penalty enforces the overall cost function to be convex. The proposed solution is based on a Bayesian formulation, whereby the point estimates are recovered using maximum a posteriori (MAP) estimation. To quantify the performance of the proposed method, various types of SAR images are used, corresponding to TerraSAR-X, COSMO-SkyMed, Sentinel-1, and ALOS2. The performance of various priors in solving the proposed inverse problem is first studied by investigating the GMC along with the L1, Lp, nuclear and total variation (TV) norms. We show that the GMC achieves the best results and we subsequently study the merits of the corresponding method in comparison to two state-of-the-art approaches for ship wake detection. The results show that our proposed technique offers the best performance by achieving 80% success rate.