Mixed Rank-Constrained Model for Simultaneous Denoising and Reconstruction of 5-D Seismic Data

Recently, studies on multidimensional seismic data interpolation through rank-constrained matrix or tensor completion have led to many effective methods, with satisfactory results. Despite the success of the rank-constrained matrix completion methods, e.g., damped rank reduction (DRR), and the rank-constrained tensor completion methods, e.g., high-order orthogonal iteration (HOOI), strong noise and highly decimated traces could still make the reconstruction results not acceptable. In this article, we find that implementing only one rank constraint to solve the multidimensional seismic data recovery problem is not sufficient. Therefore, we consider a hybrid method to reconstruct the noisy and incomplete traces based on a new mixed rank-constrained (MRC) algorithm. The proposed MRC algorithm aims to take advantage of the merits of both the rank-constrained matrix and tensor completion models to restore the missing data. We first apply the unfolding and folding operator to the 4-D spatial hypercube data. Then, for each iteration, we connect the DRR and the HOOI approaches in the same framework to solve the proposed MRC model. The proposed MRC model aims to provide an enhanced level of rank constraint to improve the signal-to-noise ratio (SNR) of the recovered data. Synthetic and field 5-D seismic data are used to compare the performance of the new method with the HOOI and DRR methods. The comparison via visual inspection and numerical analysis reveals the better performance of the proposed MRC algorithm.