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The analysis of ocean surface is widely performed using synthetic aperture radar (SAR) imagery as it yields information for wide areas under challenging weather conditions, during day or night, etc. Speckle noise constitutes however the main reason for reduced performance in applications such as classification, ship detection, target tracking and so on. This paper presents an investigation into the despeckling of SAR images of the ocean that include ship wake structures, via sparse regularisation using the Cauchy proximal operator. We propose a closed form expression for calculating the proximal operator for the Cauchy prior, which makes it applicable in generic proximal splitting algorithms. In our experiments, we simulate SAR images of moving vessels and their wakes. The performance of the proposed method is evaluated in comparison to the <tex>$L_{1}$</tex> and <tex>$TV$</tex> norm regularisation functions. The results show a superior performance of the proposed method for all the utilised images generated.

A Simulation Study to Evaluate the Performance of the Cauchy Proximal Operator in Despeckling SAR Images of the Sea Surface