Fast and Robust Low-Rank Approximation for Five-Dimensional Seismic Data Reconstruction

Abstract

Five-dimensional (5D) seismic data reconstruction becomes more appealing in recent years because it takes advantage of five physical dimensions of the seismic data and can reconstruct data with large gap. The low-rank approximation approach is one of the most effective methods for reconstructing 5D dataset. However, the main disadvantage of the low-rank approximation method is its low computational efficiency because of many singular value decompositions (SVD) of the block Hankel/Toeplitz matrix in the frequency domain. In this paper, we develop an SVD-free low-rank approximation method for efficient and effective reconstruction and denoising of the seismic data that contain four spatial dimensions. Our SVD-free rank constraint model is based on an alternating minimization strategy, which updates one variable each time while fixing the other two. For each update, we only need to solve a linear least-squares problem with much less expensive QR factorization. The SVD-based and SVD-free lowrank approximation methods in the singular spectrum analysis (SSA) framework are compared in detail, regarding the reconstruction performance and computational cost. The comparison shows that the SVD-free low-rank approximation method can obtain similar reconstruction performance as the SVD-based method but with a large computational speedup.

Low‐rank seismic data reconstruction and denoising by CUR matrix decompositions

“…The randomized QR factorization also provides flexibility regarding the actual rank, similar to the proposed CUR decompositions. Wu et al (2020) develop an SVD-free low-rank approximation method based on an alternating minimization strategy, which solves a linear least-squares problem with the less expensive QR factorization. However, the value of the rank is required because it corresponds to the dimensions of the factorization matrices.…”

“…To alleviate the cost, Oropeza and Sacchi (2011) suggest the use of a randomized SVD (R-SVD), whereas Gao et al (2013) propose the Lanczos bidiagonalization as an alternative to the SVD. Carozzi and Sacchi (2019), Wu et al (2020) and provide other SVD-free approaches for data reconstruction and noise suppression.…”

Moving target detection method based on CUR‐RPCA for missing array elements

“…To further reduce the computational complexity, a majority of researchers have aimed at how to replace the SVD decomposition. For instance, A novel method is proposed by factorization and QR decomposition to reduce the time consuming in [22]. In [23], Wu et al developed a rapid MC by exploiting the low-rank Hankel matrix factorization.…”

3D Geometry Design via End-To-End Optimization for Land Seismic Acquisition

“…Several research works have proposed to optimize seismic acquisition geometries based on data reconstruction. These traditional model-driven methods include concepts from the area of compressive sensing [2,3,4], the use of low-rank [5,6,7], and sparsity-based [8,9,10] optimization algorithms for the reconstruction of seismic traces (missing receivers) and shots (missing sources). A fundamental requirement to implement model-driven methods in geophysics is the sparsity that presumes the data is sparse under certain transforms or the low-rank that supposes the data contains redundancies.…”