Low-Rank Approximation Reconstruction of Five-Dimensional Seismic Data

Low-rank approximation has emerged as a promising technique for recovering five-dimensional (5D) seismic data, yet the quest for higher accuracy and stronger rank robustness remains a critical pursuit. We introduce a low-rank approximation method by leveraging the complete graph tensor network (CGTN) decomposition and the learnable transform (LT), referred to as the LRA-LTCGTN method, to simultaneously denoise and reconstruct 5D seismic data. In the LRA-LTCGTN framework, the LT is employed to project the frequency tensor of the original 5D data onto a small-scale latent space. Subsequently, the CGTN decomposition is executed on this latent space. We adopt the proximal alternating minimization algorithm to optimize each variable. Both 5D synthetic data and field data examples indicate that the LRA-LTCGTN method exhibits notable advantages and superior efficiency compared to the damped rank-reduction (DRR), parallel matrix factorization (PMF), and LRA-CGTN methods. Moreover, a sensitivity analysis underscores the remarkably stronger robustness of the LRA-LTCGTN method in terms of rank without any optimization procedure with respect to rank, compared to the LRA-CGTN method.