Deterministic models for wave and ship motion forecasting, based on measurements collected from wave radar, are becoming more and more appealing with the improvement of marine wave radar technologies. Although these devices are largely validated for the assessment of the characteristics of the sea spectrum, several improvements are still necessary to achieve an accurate deterministic reconstruction of the wave field in time and space. The common filtering techniques adopted for the analysis of the marine wave radar imaging are nowadays targeting the identification of the more prominent wave field features of the sea spectrum. This work instead investigates the feasibility of reconstructing the instantaneous wave field from radar imaging. To this end two different methodologies are compared. The first approach, referred to as LSQR, is a novel approach based on a regularised inversion of the radar tilt modulation model. The use of a linearised model for the wave radar imaging and a linear wave model for the sea elevation allows the derivation of a linear discrete inverse problem which is solved through a least-squares technique. The second approach, which is also the more common in the wave radar community, is based on the concept of Modulation Transfer Function (MTF). The adopted MTF approach is based on the idea of deriving a tuned MTF form a series of numerical simulation. The performances of two different approaches in inverting series of synthetic radar images derived from a known set of wave elevation time histories are then compared.
