A projection-onto-convex-sets network for 3D seismic data interpolation

Seismic data interpolation is an essential procedure in seismic data processing. However, conventional interpolation methods may generate inaccurate results due to the simplicity of assumptions, such as linear events or sparsity. In contrast, deep learning trains a deep neural network with a large data set without relying on predefined assumptions. However, the lack of physical priors in the traditional pure data-driven deep learning frameworks may cause low generalization for different sampling patterns. Inspired by the framework of projection onto convex sets (POCS), a new neural network is proposed for seismic interpolation, called POCS-Net. The forward Fourier transform, the inverse Fourier transform, and the threshold parameter in POCS are replaced by neural networks that are independent in different iterations. The threshold is trainable in POCS-Net rather than manually set. A nonnegative constraint is imposed on the threshold to make it consistent with traditional POCS. POCS-Net is essentially an end-to-end neural network with priors of a sampling pattern and a predefined iterative framework. Numerical results on 3D synthetic and field seismic data sets demonstrate the superiority of the reconstruction accuracy of the proposed method compared with the traditional and natural image-learned POCS methods.