Efficient seismic data reconstruction based on Geman function minimization

Abstract

Seismic data typically contain random missing traces because of obstacles and economic restrictions, influencing subsequent processing and interpretation. Seismic data recovery can be expressed as a low-rank matrix approximation problem by assuming a low-rank structure for the complete seismic data in the frequency-space (f-x) domain. The nuclear norm minimization (NNM) (sum of singular values) approach treats singular values equally, yielding a solution deviating from the optimal. Further, the log-sum majorization-minimization (LSMM) approach uses the nonconvex log-sum function as a rank substitution for seismic data interpolation, which is highly accurate but time-consuming. Therefore, this study proposes an efficient nonconvex reconstruction model based on the nonconvex Geman function (the nonconvex Geman low-rank (NCGL) model), involving a tighter approximation of the original rank function. Without introducing additional parameters, the nonconvex problem is solved using the Karush-Kuhn-Tucker condition theory. Experiments using synthetic and field data demonstrate that the proposed NCGL approach achieves a higher signal-to-noise ratio than the singular value thresholding method based on NNM and the projection onto convex sets method based on the data-driven threshold model. The proposed approach achieves higher reconstruction efficiency than the singular value thresholding and LSMM methods.