Deep learning for irregularly and regularly missing data reconstruction

Abstract

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. Deep learning (DL) 1 is a branch of machine learning (ML) that addresses the question of how to build computers that intelligently improve through experience 2. Recently, DL or ML, in general, enjoyed an explosive growth and showed great promise in various areas, e.g., biology 3,4 , image reconstruction 5,6 , and solid earth geoscience 7. DL is powerful for mining features or relationships from data, which is invaluable in the context of big data, as it extracts high-level information from huge volumes of data. Please refer to Goodfellow et al. 8 for a good textbook of DL. One of the most popular DL technologies is the convolutional neural network (CNN), which is at the core of most state-of-the-art DL solutions for numerous tasks 9. In recent years, deep CNNs have had stunning successes, surpassing human accuracy for hard problems such as visual recognition 6. In exploration seismology, DL or ML has been widely used in fault detection 10 , structural interpretation 11 , inversion 12 , and data interpolation 13-15 , to name a few. A more tremendous trend of developments has recently come about through the use of DL not for image analysis but for image transformation. In these cases, CNNs are trained to transform one type of image into another. Many geophysical problems can be posed as transforming an input profile into a corresponding output profile (e.g., denoising: transforming noisy data to noise-free data). Inspired by Isola et al. 16 , where DL is investigated as a general-purpose solution to image-to-image translation problems, we apply DL to missing data reconstruction with the aim of transforming an...

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