Seismic data recovery using deep targeted denoising priors in an alternating optimization framework

Abstract

The problem of recovering the complete seismic data from undersampled field-observed data is a long-term challenge. Many recent efforts to address this problem develop model-based recovery methods. However, current model-based methods cannot accurately capture inherent priors of seismic data to obtain optimal recovery results. For this issue, we have developed a novel model-based seismic data recovery method, which integrates a deep learning (DL)-based targeted denoiser into the seismic data recovery model and leverages the deep targeted denoising priors learned by this denoiser to implement high accuracy data recovery. Specifically, we first use operator-splitting technology to decouple the data-consistency term and prior constraint term in a seismic data recovery model, resulting in an alternating optimization scheme composed of a least-squares inversion subtask and a proximal minimization subtask. The DL-based targeted denoiser, a dual-channel deep denoising network (DcDDNet), is then plugged into the alternating optimization scheme as a modular component, according to the mathematical equivalence between the proximal operator and the targeted denoiser. This modular component replaces the formalized proximal minimization subtask and plays the role of an implicit prior in the recovery optimization problem. Finally, the least-squares inversion and deep denoising subtasks in the alternating optimization scheme are iteratively executed to achieve seismic data recovery. Due to the integration of the powerful DcDDNet, this method not only enjoys high flexibility and impressive generalization capability but also has high computational efficiency and excellent performance. Synthetic and field data with regular and irregular undersampling are used to evaluate the recovery capability of this method. The results demonstrate that, compared with the f- x adaptive interpolation and curvelet-based recovery methods, our method has advantages in visual and quality metrics. In addition, this method also is more practical in seismic applications because it works in the time-space domain and can handle spatial aliasing and spectral leakage.