  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.
