DL²: Dictionary learning regularized with deep learning prior for simultaneous denoising and interpolation

The dictionary learning method has been successfully applied to denoise and interpolate seismic data. However, this method cannot be used to adequately interpret weak seismic events and structural features. By combining dictionary learning and a convolutional neural network (CNN) denoiser, we constructed a new dictionary learning method regularized by a supervised denoiser (DL-SD). In addition to the sparse prior used in previous dictionary learning, the CNN denoiser learns from sizeable amounts of natural images using a deep neural network to help regularize the fine and structural features of data in the DL-SD. We used the plug-and-play alternating directional method of multipliers to solve the net-transform balanced DL-SD model. The results of simultaneous denoising and interpolation indicated that the proposed method is more effective than the FFDNet, a dictionary learning method known as the data-driven tight frame and the deep learning method.