Deep learning for irregularly and regularly missing data reconstruction

Deep learning (DL) is a powerful tool for mining features from data, which can theoretically avoid assumptions (e.g., linear events) constraining conventional interpolation methods. Motivated by this and inspired by image-to-image translation, we applied DL to irregularly and regularly missing data reconstruction with the aim of transforming incomplete data into corresponding complete data. To accomplish this, we established a model architecture with randomly sampled data as input and corresponding complete data as output, which was based on an encoder-decoder-style U-Net convolutional neural network. We carefully prepared the training data using synthetic and field seismic data. We used a mean-squared-error loss function and an Adam optimizer to train the network. We displayed the feature maps for a randomly sampled data set going through the trained model with the aim of explaining how the missing data are reconstructed. We benchmarked the method on several typical datasets for irregularly missing data reconstruction, which achieved better performances compared with a peer-reviewed Fourier transform interpolation method, verifying the effectiveness, superiority, and generalization capability of our approach. Because regularly missing is a special case of irregularly missing, we successfully applied the model to regularly missing data reconstruction, although it was trained with irregularly sampled data only.