Enhanced low-rank matrix estimation for simultaneous denoising and reconstruction of 5D seismic data

Abstract

Noise and missing traces usually influence the quality of multidimensional seismic data. Therefore, it is necessary to estimate the useful signal from its noisy observation. The damped rank-reduction (DRR) method has emerged as an effective method to reconstruct the useful signal matrix from noisy and incomplete observations. However, the higher the noise level and the larger the ratio of missing traces, the weaker the DRR operator becomes. Consequently, the estimated low-rank (LR) signal matrix includes a significant amount of residual noise that influences the following processing steps. Therefore, we focus on the problem of estimating an LR signal matrix from its noisy observation. To elaborate on the novel algorithm, we formulate an improved proximity function by mixing the moving-average filter and the arctangent penalty function. First, we apply the proximity function to the level-4 block Hankel matrix before singular-value decomposition (SVD) and, then, to singular values, during the damped truncated SVD process. The combination of the novel proximity function and the DRR framework leads to an optimization problem, which results in better recovery performance. Our algorithm aims at producing an enhanced rank-reduction operator to estimate the useful signal matrix with higher quality. Experiments are conducted on synthetic and real 5D seismic data to compare the effectiveness of our approach to the DRR approach. Our approach obtains better performance because the estimated LR signal matrix is cleaner and contains fewer artifacts compared to that reconstructed by the DRR algorithm.