Vandermonde constrained CANDECOMP/PARAFAC tensor decomposition for high-dimensional seismic data reconstruction

Abstract

High-dimensional seismic data are inevitably affected by missing traces and random noise, both of which negatively affect subsequent processing and interpretation. Methods based on the low-rank matrix or tensor decomposition are used to reconstruct seismic data under the assumption that noise-free and complete data are low rank in the frequency-space ( f- x) domain. However, the presence of missing traces and random noise increases the rank of the data matrix or tensor. We use the Vandermonde structure of exponential bases of linear events in the f- x domain, which is in accordance with the plane-wave hypothesis, and develop the Vandermonde constrained tensor CANDECOMP/PARAFAC decomposition (VCPD) method for high-dimensional seismic data reconstruction. The modified alternating direction method of the multipliers algorithm is developed, and the rank-1 matrix approximation is adopted to tackle this constrained optimization problem efficiently. Numerical examples of the synthetic data and field data indicate that the proposed VCPD method is effective and efficient for reconstructing the seismic data in the case of randomly missing with a poor signal-to-noise ratio. In addition, the VCPD method is insensitive to the selection of the tensor rank and more efficient than the related state-of-the-art methods, which should lead to wide applicability.