Tensors are useful structures when handling data that depend on more than two dimensions. By its very nature, pre-stack seismic data are multidimensional signals that can be described via a low-rank 4th order tensor in the frequency – space domain. Tensor completion strategies can be used to recover unrecorded observations and to improve the signal-tonoise ratio of prestack volumes. Tensor completion can be posed as an inverse problem and solved using convex optimization algorithms. The objective function for this problem contains a data misfit term and a term that serves to minimize the rank of the tensor. The alternating direction method of multipliers offers automatic rank determination and is used to obtain a reconstructed seismic volume. We present synthetic examples to illustrate the behaviour of the algorithm in terms of trade-off parameters that control the quality of the reconstruction.