Published as Geophysical Journal International, 209, 21-31, (2017)

Fast dictionary learning for noise attenuation of multidimensional seismic data

Yangkang Chen
% latex2html id marker 5430
\setcounter{footnote}{1}\fnsymbol{footnote}Previously: Bureau of Economic Geology
John A. and Katherine G. Jackson School of Geosciences
The University of Texas at Austin
University Station, Box X
Austin, TX 78713-8924
Currently: National Center for Computational Sciences
Oak Ridge National Laboratory
One Bethel Valley Road,
Oak Ridge, TN 37831-6008


The K-SVD algorithm has been successfully utilized for adaptively learning the sparse dictionary in 2D seismic denoising. Because of the high computational cost of many SVDs in the K-SVD algorithm, it is not applicable in practical situations, especially in 3D or 5D problems. In this paper, I extend the dictionary learning based denoising approach from 2D to 3D. 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 a 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. 3D synthetic, 2D and 3D 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.