Computed Tomography (CT) imaging technique is widely used in geological exploration, medical diagnosis and other fields. In practice, however, the resolution of CT image is usually limited by scanning devices and great expense. Super resolution (SR) methods based on deep learning have achieved surprising performance in two-dimensional (2D) images. Unfortunately, there are few effective SR algorithms for three-dimensional (3D) images. In this paper, we proposed a novel network named as three-dimensional super resolution convolutional neural network (3DSRCNN) to realize voxel super resolution for CT images. To solve the practical problems in training process such as slow convergence of network training, insufficient memory, etc., we utilized adjustable learning rate, residual-learning, gradient clipping, momentum stochastic gradient descent (SGD) strategies to optimize training procedure. In addition, we have explored the empirical guidelines to set appropriate number of layers of network and how to use residual learning strategy. Additionally, previous learning-based algorithms need to separately train for different scale factors for reconstruction, yet our single model can complete the multi-scale SR. At last, our method has better performance in terms of PSNR, SSIM and efficiency compared with conventional methods.scanning electron microscopy (SEM) image. Li proposed a voxel SR reconstruction algorithm 11 based on sparse representation, which can improve the resolution in all directions.Zhang et al. extended adjusted anchored neighborhood regression algorithm (A+) 14 , to 3D and proposed high frequency modified 3DA+ algorithm 15 , where a correlative dictionary and mapping matrix between high frequency and low frequency was established. In reconstruction stage, the matched dictionary atom and mapping matrix were searched for each input of the 3D block to complete SR.Unfortunately, the aforementioned algorithms are focused on 2D images, in view of the fact of 3D-CT images of rock, the following issues remain to be solved: First, the computational intensity and memory of 3D image data is far greater than the 2D images, so the method to handle with 2D images can't be directly transferred to 3D model; Second, CT samples are not as convenient as 2Dimages to obtain, that is to say, it's not easy to get substantial alignments of rock CT samples to training network. In addition, CT image of rock has the characteristics of low contrast, single texture, and complex pore structure, which all bring difficulty to task of SR; Third, during training network and reconstruction stage, the calculation and time complexity have to be taken account to ensure our work can be carried out on the general computing equipment. Hence, it is desirable to devise a new network to cope with SR for voxel images.In order to enhance resolution of CT images of rock from three directions (i.e., x, y ,z), we propose a novel network, termed as 3D super-resolution convolutional neural network (3DSRCNN), to promote resolution for volumetric images. Bef...

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Porous media are ubiquitous in both nature and engineering applications, thus their modelling and understanding is of vital importance. In contrast to direct acquisition of three-dimensional (3D) images of such medium, obtaining its sub-region (s) like two-dimensional (2D) images or several small areas could be much feasible. Therefore, reconstructing whole images from the limited information is a primary technique in such cases. Specially, in practice the given data cannot generally be determined by users and may be incomplete or partially informed, thus making existing reconstruction methods inaccurate or even ineffective. To overcome this shortcoming, in this study we proposed a deep learning-based framework for reconstructing full image from its much smaller sub-area(s). Particularly, conditional generative adversarial network (CGAN) is utilized to learn the mapping between input (partial image) and output (full image). To preserve the reconstruction accuracy, two simple but effective objective functions are proposed and then coupled with the other two functions to jointly constrain the training procedure. Due to the inherent essence of this illposed problem, a Gaussian noise is introduced for producing reconstruction diversity, thus allowing for providing multiple candidate outputs. Extensively tested on a variety of porous materials and demonstrated by both visual inspection and quantitative comparison, the method is shown to be accurate, stable yet fast (∼ 0.08s for a 128 × 128 image reconstruction). We highlight that the proposed approach can be readily extended, such as incorporating any user-define conditional data and an arbitrary number of object functions into reconstruction, and being coupled with other reconstruction methods.

Digital rock imaging plays an important role in studying the microstructure and macroscopic properties of rocks, where microcomputed tomography (MCT) is widely used. Due to the inherent limitations of MCT, a balance should be made between the field of view (FOV) and resolution of rock MCT images-a large FOV at low resolution (LR) or a small FOV at high resolution (HR). However, large FOV and HR are both expected for reliable analysis results in practice. Super-resolution (SR) is an effective solution to break through the mutual restriction between the FOV and resolution of rock MCT images, for it can reconstruct an HR image from a LR observation. Most of the existing SR methods cannot produce satisfactory HR results on real-world rock MCT images. One of the main reasons for this is that paired images are usually needed to learn the relationship between LR and HR rock images. However, it is challenging to collect such a dataset in a real scenario. Meanwhile, the simulated datasets may be unable to accurately reflect the model in actual applications. To address these problems, we propose a cycle-consistent generative adversarial network (CycleGAN)-based SR approach for real-world rock MCT images, namely, SRCycleGAN. In the off-line training phase, a set of unpaired rock MCT images is used to train the proposed SRCycleGAN, which can model the mapping between rock MCT images at different resolutions. In the on-line testing phase, the resolution of the LR input is enhanced via the learned mapping by SRCycleGAN. Experimental results show that the proposed SRCycleGAN can greatly improve the quality of simulated and real-world rock MCT images. The HR images reconstructed by SRCycleGAN show good agreement with the targets in terms of both the visual quality and the statistical parameters, including the porosity, the local porosity distribution, the two-point correlation function, the lineal-path function, the two-point cluster function, the chord-length distribution function, and the pore size distribution. Large FOV and HR rock MCT images can be obtained with the help of SRCycleGAN. Hence, this work makes it possible to generate HR rock MCT images that exceed the limitations of imaging systems on FOV and resolution.

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