This Ph.D. thesis focuses on reconstructing satellite images of the ocean surface from sparse and noisy measurements. Our objective is the reconstruction of the Sea Surface Height (SSH), an important variable used to estimate surface currents. It is retrieved through nadir-pointing altimeters, leaving important observation gaps due to their remote sensing technology. Complete SSH maps are produced using linear Optimal Interpolations with low effective resolution. On the other hand, Sea Surface Temperature (SST) products have much higher data coverage, and SST is physically linked to geostrophic currents through advection.
This thesis explores deep learning algorithms to estimate SSH fields. Relying on years of data from the simulation and observations, deep neural networks are able to learn complex relationships between SSH and SST variables. Using these algorithms and SST observations, we first enhance SSH mapping from a downscaling perspective on a physical simulation. Then, we tackle the SSH interpolation problem on simulation and observation data, with a particular focus on how to transfer the learning in operational settings. Finally, we adapt our method to produce near real time and forecast estimations.