Robust fast dictionary learning for seismic noise attenuation

Dictionary learning has been intensively applied to process multi-channel seismic data due to its adaptively learned basis atoms that are data driven. Traditionally, dictionary learning is mostly used to attenuate random noise in the literature since the dictionary update operation is not sensitive to Gaussian noise. However, when dictionary learning is applied to seismic data containing strong erratic noise, which does not follow the Gaussian distribution, its performance greatly deteriorates. In this paper, we propose a novel robust dictionary learning method for dealing with both random and erratic noise. We formulate the dictionary-learning-sbased denoising problem as an iterative process. During each iteration, we gradually diminish the effect of the erratic noise and make the denoising problem more Gaussian type. Considering the computational overburden of the classic K-singular value decomposition algorithm due to many iterations, we substitute the K-singular value decomposition algorithm with an efficient algorithm, which does not require the singular value decomposition operation. We apply the proposed method to several synthetic and field datasets and obtain good performance, which demonstrates its potential for wide application.