Tensor Decomposition Dictionary Learning With Low-Rank Regularization for Seismic Data Denoising

Sparse transforms and dictionary learning (DL) play important roles in seismic data denoising. For high-dimensional data, most of these methods consider the data as a combination of 2-D data slices and denoise each 2-D data slice to obtain final denoising results. However, this ignores the structural features of high-dimensional seismic data. Tensor decomposition can utilize high-dimensional features of data, and it includes event features of data in horizontal, lateral, and front directions. Meanwhile, high-dimensional seismic data often exhibit analogous textural structures between slices in the inline or crossline. Thus, the learned dictionaries present similar over-complete atoms with redundant atoms in these directions. To overcome this problem, we propose a method, called tensor decomposition dictionary learning (TDDL) method. We decompose the data into front direction and then learn dictionaries in the front slices. Due to a high correlation in the characteristics of the seismic events, the low rankness of the coding coefficients is used to obtain the denoising data. In the numerical experiments, the proposed method is tested on 3-D and 5-D seismic data. The results show that the proposed method gets better denoising performance than the data-driven tight frame (DDTF) DL and curvelet transform methods.