Reconstruction of seismic data via tensor completion

We describe the use of a higher-order singular value decomposition (HOSVD) in the reconstruction of seismic volumes. Seismic data in the frequency - space domain are represented via a 4-th order tensor. We present an iterative algorithm that permits to simultaneously de-noise and recover missing observations. The algorithm assumes that 4D spatial data can be represented by a low-rank tensor computed via the Higher-Order Singular Value Decomposition (HOSVD).