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For numerous domains, including for instance earth observation, medicalimaging, astrophysics,..., available image and signal datasets often involveirregular space-time sampling patterns and large missing data rates. Thesesampling properties may be critical to apply state-of-the-art learning-based(e.g., auto-encoders, CNNs,...), fully benefit from the available large-scaleobservations and reach breakthroughs in the reconstruction and identificationof processes of interest. In this paper, we address the end-to-end learning ofrepresentations of signals, images and image sequences from irregularly-sampleddata, i.e. when the training data involved missing data. From an analogy toBayesian formulation, we consider energy-based representations. Two energyforms are investigated: one derived from auto-encoders and one relating toGibbs priors. The learning stage of these energy-based representations (orpriors) involve a joint interpolation issue, which amounts to solving an energyminimization problem under observation constraints. Using aneural-network-based implementation of the considered energy forms, we canstate an end-to-end learning scheme from irregularly-sampled data. Wedemonstrate the relevance of the proposed representations for differentcase-studies: namely, multivariate time series, 2D images and image sequences.

End-to-end learning of energy-based representations for irregularly-sampled signals and images