Efficient Convolutional Sparse Coding Based on Penalized Weighted Least Squares for Seismic Data Denoising

Recently, convolutional sparse coding (CSC) has been successfully applied to seismic data denoising. CSC differs from traditional dictionary learning methods based on patching schemes in that it can directly process the whole data and capture correlations between local neighborhoods. However, the learned filters by CSC may contain inaccurate features resulting in the structure loss of data, and solving CSC problems has a heavy computational burden. To optimize these problems, we investigate the denoising accuracy of the CSC model and introduce CSC as a regularization term into the penalized weighted least-squares (PWLSs) framework. In particular, we design an effective method to solve the problem of updating sparse feature maps, which improves computational efficiency. Combining the above two points, we propose an efficient CSC (ECSC) model for random noise attenuation of seismic data. The numerical experiments on synthetic data and field data demonstrate that ECSC performs better than the K-singular value decomposition (K-SVD) algorithm, sequential generalized K-means (SGK) algorithm, and fast and flexible CSC (FF-CSC) in seismic data denoising performance and computational efficiency.