Fast dictionary learning for 3D simultaneous seismic data reconstruction and denoising

Simultaneous seismic data reconstruction and denoising is a hot research topic. The sparse representation method based on dictionary learning is one of the most effective methods to reconstruct seismic data and suppress noise. Sparse dictionary traditionally uses the K-means singular value decompositions (K-SVD) method for learning. However, the main disadvantage of K-SVD is that it requires many singular value decompositions (SVDs), which is low in computational efficiency and not suitable for practical applications, especially in highdimensional problems. To address the computational efficiency problem of K-SVD, we propose a fast dictionary learning method based on sequence generalized K-means (SGK) algorithm for efficient reconstruction and denoising of 3D seismic data. In SGK algorithm, dictionary atoms are updated by arithmetic average of several training signals instead of singular value decomposition in the K-SVD algorithm. The performance of the two methods is verified by 3D numerical examples. The results demonstrate that the proposed reconstruction and denoising method using SGK can achieve comparable performance as the K-SVD method but significantly improve the computational efficiency.