Structure-Oriented CUR Low-Rank Approximation for Random Noise Attenuation of Seismic Data
Peng Lin, Suping Peng, Yang Xiang, Chuangjian Li, Xiaoqin Cui, Wenkai Zhang
Abstract
Random noise attenuation is one of the most essential steps in seismic data processing, and effective denoising methods can significantly improve the accuracy of structural imaging and data inversion. To address this issue, we propose a novel low-rank approximation method that uses a CUR matrix decomposition algorithm instead of the traditional truncated singular-value decomposition (SVD). The low-rank method is applied along the structural direction of seismic data produced by plane-wave structural prediction to strengthen the low-rank property. The CUR decomposition exhibits a matrix as a product of three matrices, C, U, and R, to obtain a low-rank approximation. The decomposed matrices are formed by randomly selecting a subset of columns and rows from the data matrix. The subspace sampling algorithm is considered as a column selection principle to compute CUR decompositions. The proposed CUR-based low-rank denoising method is directly exploited to perform low-rank approximation in the Hankelization space, thus avoiding the time-consuming SVD. To improve the accuracy of slope estimation, a robust plane-wave destruction (PWD) algorithm with nonstationary shaping regularization is provided to enhance the slope estimation of noisy data. Synthetic and field examples are used to demonstrate the effectiveness performance of the proposed CUR-based low-rank denoising method both in eliminating seismic random noise and improving computational efficiency.