  In this paper, we analyse synthetic aperture radar (SAR) images of the sea
surface using an inverse problem formulation whereby Radon domain information
is enhanced in order to accurately detect ship wakes. This is achieved by
promoting linear features in the images. For the inverse problem-solving stage,
we propose a penalty function, which combines the dual-tree complex wavelet
transform (DT-CWT) with the non-convex Cauchy penalty function. The solution to
this inverse problem is based on the forward-backward (FB) splitting algorithm
to obtain enhanced images in the Radon domain. The proposed method achieves the
best results and leads to significant improvement in terms of various
performance metrics, compared to state-of-the-art ship wake detection methods.
The accuracy of detecting ship wakes in SAR images with different frequency
bands and spatial resolution reaches more than 90%, which clearly demonstrates
an accuracy gain of 7% compared to the second-best approach.
