Multistep Super Resolution Double-U-net (SRDUN) for enhancing the resolution of Berea sandstone images

Abstract

Digital Rock Physics (DRP) has opened a new avenue through the microscale world of rocks leading to more detailed inferences. However, High Resolution (HR) images are problematic from several aspects such as low field of view, huge memory and long time and high cost of image acquisition. Recent advances in Machine Learning (ML) and especially Convolutional Neural Networks (CNN) highly improved the ability of producing HR images from their Low Resolution (LR) counterparts known as Super Resolution (SR) images. In this procedure, the scale-difference between LR and HR images is a key parameter, while a high scale-difference leads to unreliable results regardless of the method. To overcome such a problem, we aim to both propose a multiscale procedure and introduce an efficient network namely Super Resolution Double-U-net (SRDUN). To this end, unlike conventional studies where LR images are synthetically produced from HR images, we capture these images from a Berea sandstone individually in five different scales (16.263, 12.922, 9.499, 5.775 and 3.501 μm for samples with a side of 10, 8, 6, 4 and 2-mm). Then, the SRDUN is introduced, where a first U-net is used to store feature maps of HR images and are imported in a second U-net as informative skip connections. Results show SRDUN could perform more accurate than common networks for small scale-differences. However, when it comes to high scale-differences it becomes more complicated. We propose a multistep procedure, where several mid-step SRDUNs are used to fill the gap of information. Results of this procedure reveal that the multistep procedure could perform much better than the direct approach. These results are then demonstrated by some computations of reservoir parameters such as porosity, pore equivalent diameter distribution, morphometric properties and permeability. Porosity and permeability computations showed that the error of computed values from SR images is increased by increasing scale-difference, however, the multistep procedure leads to more reliable results. The multistep procedure could preserve better the pore size distribution, however, in morphometric properties, the direct approach performs better since the multistep procedure suffers from a smoothing effect.