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Simultaneous-source data can be adequately separated using an inversion formulation. To recover component shot records, we formulate the data-separation problem as a simultaneous Radon inversion problem. By minimizing the resulting objective function with a robust hybrid solver, we obtain high-quality estimates of the component shot records. Furthermore, regularization with directional Laplacians improves the data quality. In our approach, we estimate a single model that predicts all recorded data, and we treat all components of the recorded data as signal. Within limits of operational possibilities, our method can be applied to any number of sources within a single survey and can be easily extended to multiple (time-lapse) surveys. Using 2D sections extracted from the 3D SEAM geophysical model, we show that our method can give results of comparable quality to the original independent shot records.