3-D Random Noise Attenuation Using Stable CUR Matrix Decomposition

The low-rank property of seismic data has been successfully used for attenuating seismic random noise using a rank-reduction processing; however, traditional rank-reduction methods based on truncated singular-value decomposition (TSVD) require exact rank estimation, i.e., denoised results are closely associated with rank selection. To address this problem, we propose a novel and effective rank-reduction method for 3-D random noise attenuation that introduces CUR matrix decomposition to the multichannel singular-spectrum analysis (MSSA) for performing low-rank approximation as an alternative to the traditional TSVD. CUR matrix decomposition expresses a data matrix as a product of three matrices by selecting a small number of columns and rows from the data matrix to approximate low-rank components. A subspace column selection algorithm is used to randomly select columns and rows from a Hankel matrix and construct three decomposed matrices in the frequency-space domain. A stable CUR decomposition algorithm is further exploited to eliminate the potential instability problem when obtaining the CUR. The random column selection strategy of the CUR matrix decomposition can effectively obviate the exact rank requirement and achieve superior low-rank approximation results. We present 3-D synthetic and field examples to demonstrate the effectiveness of the proposed CUR-based low-rank approximation in highlighting useful signals and attenuating random noise. Results obtained using CUR matrix decomposition are comparable to those obtained using traditional low-rank methods.