Nuclear norm minimization and tensor completion in exploration seismology

We consider the problem of multidimensional seismic data signal recovery and noise attenuation. These data are multi-dimensional signals that can be described via a low-rank fourth-order tensor in the frequency-space domain. Tensor completion strategies can be used to recover unrecorded observations and to improve the signal-to-noise ratio of seismic data volumes. Tensor completion is posed as an inverse problem and solved via a convex optimization algorithm where a misfit function is minimized in conjunction with the nuclear norm of the tensor. This formulation offers automatic rank determination. We illustrate the performance of the algorithm with a synthetic example and with a real data set obtained by an onshore seismic survey.