The dictionary learning method has been successfully ap-plied 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) de-noiser, we have constructed a new dictionary learning method regularized by a supervised denoiser (DL-SD). In addition to the sparse prior used in previous dictionary learn-ing, the CNN denoiser learns from sizeable amounts of natu-ral images using a deep neural network to help regularize the fine and structural features of data in the DL-SD. We use the plug-and-play alternating directional method of multipliers to solve the net-transform balanced DL-SD model. The re-sults of simultaneous denoising and interpolation indicates that the proposed method is more effective than a deep learn-ing method called the FFDNet and a dictionary learning method known as the data-driven tight frame.
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