Sparse prior-net: A sparse prior-based deep network for seismic data interpolation

Seismic data interpolation plays a crucial role in obtaining dense and regularly sampled data, contributing to improving the quality of seismic data in seismic exploration. Sparsity-promoting methods use a two-step iteration to gradually recover missing traces, by exploiting the sparsity representation of seismic data in transform domains, such as Fourier, wavelet, and curvelet transform, within the framework of the projection onto convex sets (POCS). In the first step, the missing traces are restored by applying the thresholding shrinkage to the transform coefficients. In the second step, the observed data are inserted into the updated result. However, this method relies on a preselected transform and lacks the capability to adaptively capture sparse representations. In addition, determining the optimal threshold parameters can pose difficulties. These limitations yield unsatisfactory reconstruction results. To address this issue, we propose a novel approach called sparse prior-based seismic interpolation network (SP-net) that combines the sparsity-promoting method with a deep neural network. Unlike traditional end-to-end networks, our proposed neural network integrates the widely used POCS method into its architecture, enabling automatic learning of the sparse transform, and threshold parameters from the training data set. By combining the merits of the sparsity-promoting techniques and data-driven deep-learning approaches, SP-net achieves enhanced adaptability and more accurate interpolation results. Through experiments conducted on synthetic and field seismic data, we demonstrate the effectiveness of our proposed method.