Seismic data denoising using convolutional sparse coding with an efficient alternating direction multipliers minimization algorithm

Abstract

During the acquisition of field seismic data, it is unavoidable to encounter random noise, and this will have an impact on the subsequent processing and interpretation of the seismic data. Lately, dictionary learning has demonstrated significant advancements in seismic data denoising. The most common method among patch-based dictionary learning algorithms is the K-singular value decomposition (K-SVD) method, which is a learning method based on patching schemes and processes data on overlapping patches without considering the complete data and the global features. In order to optimize these problems, we use convolutional sparse coding (CSC) for seismic data denoising, which can process the global data and capture the correlation between local neighborhoods. We propose the convolutional sparse coding based on an efficient alternating direction multipliers minimization (ADMM) for noise attenuation in seismic data. This CSC with efficient ADMM algorithm is capable of effectively addressing the subproblem of convolutional least-squares fitting, which reduces the complexity of the algorithm and converges to a valid solution. We accomplish the seismic data denoising using the learned filters and the corresponding sparse feature maps. The numerical experimental results on synthetic data and field data demonstrate that in comparison to fast and flexible convolutional sparse coding (FF-CSC) and K-SVD, the proposed method has more advantages in denoising performance and computational efficiency.