Five-dimensional Seismic Data Reconstruction and Denoising based on A Preconditioned Riemannian Gradient Descent

Seismic data acquisition routinely suffers from insufficient spatial sampling and noise contamination, both of which degrade imaging quality and interpretation accuracy. Reconstruction methods based on low-rank assumptions can recover missing traces effectively, yet they incur high computational cost from large-scale singular value decomposition (SVD), which limits their practical efficiency. To address this bottleneck, we develop a preconditioned Riemannian gradient descent (PRGD) method based five-dimensional (5D) seismic data reconstruction. Within a Riemannian optimization framework, PRGD weights the gradient by a data-driven preconditioner, thereby reducing sensitivity to step-size selection. Simultaneously, the method exploits the low-rank structure of the tangent space of the manifold of low-rank matrices, avoiding large-scale SVD and considerably lowering computational complexity. Experiments on synthetic and field data demonstrate that, compared with the classical damped rank-reduction (DRR) method, PRGD achieves higher reconstruction accuracy in fewer iterations. It requires approximately one-seventh of the computation time of DRR and maintains superior reconstruction performance under 80% to 90% missing-trace ratios.