Satellite-derived products are of key importance for the high-resolution monitoring of the ocean surface on a global scale. Due to the sensitivity of spaceborne sensors to the atmospheric conditions as well as the associated spatio-temporal sampling, ocean remote sensing data may be subject to high-missing data rates. The spatio-temporal interpolation of these data remains a key challenge to deliver L4 gridded products to end-users. Whereas operational products mostly rely on model-driven approaches, especially optimal interpolation based on Gaussian process priors, the availability of large-scale observation and simulation datasets calls for the development of novel data-driven models. This study investigates such models. We extend the recently introduced analog data assimilation to high-dimensional spatio-temporal fields using a multi-scale patch-based decomposition. Using an Observing System Simulation Experiment (OSSE) for sea surface temperature, we demonstrate the relevance of the proposed data-driven scheme for the real missing data patterns of the high-resolution infrared METOP sensor. It has resulted in a significant improvement w.r.t. state-of-the-art techniques in terms of interpolation error (about 50\% of relative gain) and spectral characteristics for horizontal scales smaller than 100km. We further discuss the key features and parameterizations of the proposed data-driven approach as well as its relevance with respect to classical interpolation techniques.