2-D Seismic random noise attenuation via self-paced nonnegative dictionary learning

The sparse representation of a seismic signal plays a significant role to suppress random noise in the seismic data. Dictionary learning (DL) is an effective tool to find a suitable sparse representation of a seismic signal. As an unsupervised DL, non-negative matrix factorization (NMF) has been widely used for attenuating random noise in seismic data during recent years. However, due to the nonconvexity of the NMF, most of the NMF methods might suffer from bad local minima, especially for seismic data with heavy noise. To solve this issue, we propose a workflow to suppress seismic random noise in the time-space domain, named self-paced nonnegative dictionary learning (SPNDL). The SPNDL is implemented by incorporating the self-paced learning (SPL) method with the NMF. Inspired by the learning way of humans and animals, the SPL selects the training samples automatically from easy to complex. Based on the SPL theory, a valid seismic data can be recovered by training the sample points with the high signal-To-noise ratio (SNR) values, and then gradually including the sample points with the low SNR values into NMF training. Our proposed SPNDL solves the bad local minima issue and obtains a robust denoised result. The potential of the proposed SPNDL method is demonstrated by both examples of a synthetic data and a field data.