We describe the use of a higher-order singular value decomposition (HOSVD) in the regularization of pre-stack seismic volumes. Pre-stack seismic data in the frequency — space domain are represented with a 4-th order tensor. We present an iterative algorithm that permits to simultaneously de-noise and recover missing observations, assuming that pre-stack 4D spatial data can be represented by a low-rank tensor computed via the HOSVD. Contrary to many multidimensional reconstruction methods, the proposed algorithm operates quite well in the presence of curved events. Synthetic and real data are used to test the proposed algorithm.