Nonlocal Weighted Robust Principal Component Analysis for Seismic Noise Attenuation

Seismic data are usually contaminated by various noises. Noise suppression plays an important role in seismic processing. In this article, we propose a new denoising method based on the nonlocal weighted robust principal component analysis (RPCA). First, seismic data are divided into many patches and grouped based on the nonlocal similarity. For each group, then, we establish a similar block matrix and set up the objective function of the RPCA. Next, we introduce the iterative log-thresholding algorithm into the augmented Lagrangian method to solve the problem. Furthermore, varying weights are specified to different singular values when minimizing the objective function. Finally, aggregating all recovered matrices can obtain the denoised seismic data. The proposed method considers the nonlocal similarity and adaptively sets weights with local noise variance. It performs well also owing to the superiority of the iterative log-thresholding method. The presented method is assessed using a synthetic seismic section with several crossover events. We also apply this novel approach to a real seismic data, which shows good results. Comparison with other approaches reveals the effectiveness of the proposed approach.