Sea surface height (SSH) is a key geophysical parameter for monitoring and studying meso-scale surface ocean dynamics. For several decades, the mapping of SSH products at regional and global scales has relied on nadir satellite altimeters, which provide one-dimensional-only along-track satellite observations of the SSH. The Surface Water and Ocean Topography (SWOT) mission deploys a new sensor that acquires for the first time wide-swath two-dimensional observations of the SSH. This provides new means to observe the ocean at previously unresolved spatial scales. A critical challenge for the exploiting of SWOT data is the separation of the SSH from other signals present in the observations. In this paper, we propose a novel learning-based approach for this SWOT calibration problem. It benefits from calibrated nadir altimetry products and a scale-space decomposition adapted to SWOT swath geometry and the structure of the different processes in play. In a supervised setting, our method reaches the state-of-the-art residual error of ~1.4cm while proposing a correction on the entire spectral from 10km to 1000k
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