Irregular spatial sampling and rank reduction: interpolation by joint low-rank and sparse inversion

Until now, noise attenuation and interpolation processes based on rank reduction needed spatially regular, or at least binned, data. Here, we show how the low-rank signal model in joint low-rank and sparse inversion (JLRSI), a recently proposed convex optimization framework for simultaneous random plus erratic noise attenuation and interpolation, can be extended to spatially irregular data by appropriately modifying the inverse problem formulation. Benefits of considering the true spatial locations of seismic traces for the quality of the signal reconstruction are illustrated on a three-dimensional regularization and interpolation example on real land data.