A robust data interpolation method using curvelets frames is presented. The advantage of this method is that curvelets arguably provide an optimal sparse representation for solutions of wave equations with smooth coefficients. As such curvelets frames circumvent - besides the assumption of caustic-free data - the necessity to make parametric assumptions (e.g. through linear/parabolic Radon or demigration) regarding the shape of events in seismic data. A brief sketch of the theory is provided as well as a number of examples on synthetic and real data.