Nonconvex Tensor Completion for 5-D Seismic Data Reconstruction

Abstract

Multidimensional pre-stack seismic data reconstruction can be viewed as a low-rank tensor completion problem. Recently, the nuclear norm has been widely used as a convex surrogate of the tensor rank function for low-rank tensor recovery and has been successfully applied to 5D seismic data reconstruction. However, solving the nuclear norm-based relaxed convex problem typically leads to a suboptimal solution of the original rank minimization problem, often degrading the reconstruction performance. In this study, to seek solutions to the aforementioned problems, we established a non-convex logDet function as a smooth approximation for the tensor rank instead of the convex tensor nuclear norm and applied it to solve the 5D seismic data reconstruction problem. Thereafter, we propose solving the obtained non-convex relaxation problem using an alternating direction method of multipliers (ADMM) algorithm. Numerical experiments of our approach on synthetic 5D seismic data demonstrated remarkable reconstruction performance compared with the performances of HOSVD, nulear norm, and PMF methods in terms of visual examination and numerical test. We further illustrate the performance of the proposed method using a land data survey.