  We consider the problem of recovering the surface wave profile from noisy
bottom pressure measurements with (\textit{a priori} unknown) arbitrary
pressure at the surface. Without noise, the direct approach developed in
\cite{clamond2023steady} provides an effective way to recover the sea surface.
However, the assumption of analyticity for the measurement renders this method
inefficient in the presence of noise. Therefore, we introduce an optimisation
procedure based on the minimisation of a distance between a recovered bottom
pressure and its measurement. Such method proves to be well-designed to handle
perturbed signals. We illustrate the effectiveness of this approach in the
recovery of gravity-capillary waves from unfiltered noisy data.
