Computing device, computer instructions and method for processing input seismic data d associated with a surveyed subsurface. The method includes: receiving the input seismic data d recorded in a first domain by seismic receivers that travel in water, the input seismic data d including pressure data and particle motion data; generating a model p in a second domain, which is different from the first domain, to describe the input seismic data d; processing the model p to generate an output seismic dataset with attenuated noise; and generating an image of the surveyed subsurface based on the output seismic dataset.