Random noise attenuation with weak feature preservation via total variation regularization

Dictionary learning (DL) methods have been successfully applied to seismic data denoising. However, when the noise is strong, weak signals cannot be well preserved. Considering the characteristics of seismic data in the spatial-time domain, we propose a dictionary learning method with total variation regularization (DLTV). The DLTV method consists of two steps. The first step is to learn the dictionary; it uses the sparse feature of the data in the dictionary domain and the learned dictionary contains data features. The second step is to use the augmented Lagrange multiplier method to restore the data, and total variation regularization to preserve the weak signal by sampling data information around it. An example with seismic data shows that the proposed method retains the weak features better than the traditional F-X deconvolution (FX-Decon) method and the data-driven tight frame method (DDTF).