RETRACTED: Fast dictionary learning for noise attenuation of multidimensional seismic data (Publication with Expression of Concern. See vol. 221, pg. 2053, 2020) (Retracted article. See vol. 222, pg. 1896, 2020)

The K-SVD algorithm has been successfully utilized for adaptively learning the sparse dictionary in 2-D seismic denoising. Because of the high computational cost of many singular value decompositions (SVDs) in the K-SVD algorithm, it is not applicable in practical situations, especially in 3-D or 5-D problems. In this paper, I extend the dictionary learning based denoising approach from 2-D to 3-D. To address the computational efficiency problem in K-SVD, I propose a fast dictionary learning approach based on the sequential generalized K-means (SGK) algorithm for denoising multidimensional seismic data. The SGK algorithm updates each dictionary atom by taking an arithmetic average of several training signals instead of calculating an SVD as used in K-SVD algorithm. I summarize the sparse dictionary learning algorithm using K-SVD, and introduce SGK algorithm together with its detailed mathematical implications. 3-D synthetic, 2-D and 3-D field data examples are used to demonstrate the performance of both K-SVD and SGK algorithms. It has been shown that SGK algorithm can significantly increase the computational efficiency while only slightly degrading the denoising performance.