Attention-based 3D CNN with Multi-layer Features for Alzheimer's Disease Diagnosis using Brain Images.

Structural MRI and PET imaging play an important role in the diagnosis of Alzheimer's disease (AD), showing the morphological changes and glucose metabolism changes in the brain respectively. The manifestations in the brain image of some cognitive impairment patients are relatively inconspicuous, for example, it still has difficulties in achieving accurate diagnosis through sMRI in clinical practice. With the emergence of deep learning, convolutional neural network (CNN) has become a valuable method in AD-aided diagnosis, but some CNN methods cannot effectively learn the features of brain image, making the diagnosis of AD still presents some challenges. In this work, we propose an end-to-end 3D CNN framework for AD diagnosis based on ResNet, which integrates multi-layer features obtained under the effect of the attention mechanism to better capture subtle differences in brain images. The attention maps showed our model can focus on key brain regions related to the disease diagnosis. Our method was verified in ablation experiments with two modality images on 792 subjects from the ADNI database, where AD diagnostic accuracies of 89.71% and 91.18% were achieved based on sMRI and PET respectively, and also outperformed some state-of-the-art methods.

Three-dimensional reconstruction of granular porous media based on deep generative models.

Reconstruction of microstructure in granular porous media, which can be viewed as granular assemblies, is crucial for studying their characteristics and physical properties in various fields concerned with the behavior of such media, including petroleum geology and computational materials science. In spite of the fact that many existing studies have investigated grain reconstruction, most of them treat grains as simplified individuals for discrete reconstruction, which cannot replicate the complex geometrical shapes and natural interactions between grains. In this work, a hybrid generative model based on a deep-learning algorithm is proposed for high-quality three-dimensional (3D) microstructure reconstruction of granular porous media from a single two-dimensional (2D) slice image. The method extracts 2D prior information from the given image and generates the grain set as a whole. Both a self-attention module and effective pattern loss are introduced in a bid to enhance the reconstruction ability of the model. Samples with grains of varied geometrical shapes are utilized for the validation of our method, and experimental results demonstrate that our proposed approach can accurately reproduce the complex morphology and spatial distribution of grains without any artificiality. Furthermore, once the model training is complete, rapid end-to-end generation of diverse 3D realizations from a single 2D image can be achieved.

Multi-modal graph neural network for early diagnosis of Alzheimer's disease from sMRI and PET scans.

In recent years, deep learning models have been applied to neuroimaging data for early diagnosis of Alzheimer's disease (AD). Structural magnetic resonance imaging (sMRI) and positron emission tomography (PET) images provide structural and functional information about the brain, respectively. Combining these features leads to improved performance than using a single modality alone in building predictive models for AD diagnosis. However, current multi-modal approaches in deep learning, based on sMRI and PET, are mostly limited to convolutional neural networks, which do not facilitate integration of both image and phenotypic information of subjects. We propose to use graph neural networks (GNN) that are designed to deal with problems in non-Euclidean domains. In this study, we demonstrate how brain networks are created from sMRI or PET images and can be used in a population graph framework that combines phenotypic information with imaging features of the brain networks. Then, we present a multi-modal GNN framework where each modality has its own branch of GNN and a technique that combines the multi-modal data at both the level of node vectors and adjacency matrices. Finally, we perform late fusion to combine the preliminary decisions made in each branch and produce a final prediction. As multi-modality data becomes available, multi-source and multi-modal is the trend of AD diagnosis. We conducted explorative experiments based on multi-modal imaging data combined with non-imaging phenotypic information for AD diagnosis and analyzed the impact of phenotypic information on diagnostic performance. Results from experiments demonstrated that our proposed multi-modal approach improves performance for AD diagnosis. Our study also provides technical reference and support the need for multivariate multi-modal diagnosis methods.

Deep learning method of stochastic reconstruction of three-dimensional digital cores from a two-dimensional image.

Digital cores can characterize the true internal structure of rocks at the pore scale. This method has become one of the most effective ways to quantitatively analyze the pore structure and other properties of digital cores in rock physics and petroleum science. Deep learning can precisely extract features from training images for a rapid reconstruction of digital cores. Usually, the reconstruction of three-dimensional (3D) digital cores is performed by optimization using generative adversarial networks. The training data required for the 3D reconstruction are 3D training images. In practice, two-dimensional (2D) imaging devices are widely used because they can achieve faster imaging, higher resolution, and easier identification of different rock phases, so replacing 3D images with 2D ones avoids the difficulty of acquiring 3D images. In this paper, we propose a method, named EWGAN-GP, for the reconstruction of 3D structures from a 2D image. Our proposed method includes an encoder, a generator, and three discriminators. The main purpose of the encoder is to extract statistical features of a 2D image. The generator extends the extracted features into 3D data structures. Meanwhile, the three discriminators have been designed to gauge the similarity of morphological characteristics between cross sections of the reconstructed 3D structure and the real image. The porosity loss function is used to control the distribution of each phase in general. In the entire optimization process, a strategy using Wasserstein distance with gradient penalty makes the convergence of the training process faster and the reconstruction result more stable; it also avoids the problems of gradient disappearance and mode collapse. Finally, the reconstructed 3D structure and the target 3D structure are visualized to ascertain their similar morphologies. The morphological parameter indicators of the reconstructed 3D structure were consistent with those of the target 3D structure. The microstructure parameters of the 3D structure were also compared and analyzed. The proposed method can achieve accurate and stable 3D reconstruction compared with classical stochastic methods of image reconstruction.

Improved recurrent generative model for reconstructing large-size porous media from two-dimensional images.

Modeling the three-dimensional (3D) structure from a given 2D image is of great importance for analyzing and studying the physical properties of porous media. As an intractable inverse problem, many methods have been developed to address this fundamental problems over the past decades. Among many methods, the deep learning-(DL) based methods show great advantages in terms of accuracy, diversity, and efficiency. Usually, the 3D reconstruction from the 2D slice with a larger field-of-view is more conducive to simulate and analyze the physical properties of porous media accurately. However, due to the limitation of reconstruction ability, the reconstruction size of most widely used generative adversarial network-based model is constrained to 64^{3} or 128^{3}. Recently, a 3D porous media recurrent neural network based method (namely, 3D-PMRNN) (namely 3D-PMRNN) has been proposed to improve the reconstruction ability, and thus the reconstruction size is expanded to 256^{3}. Nevertheless, in order to train these models, the existed DL-based methods need to down-sample the original computed tomography (CT) image first so that the convolutional kernel can capture the morphological features of training images. Thus, the detailed information of the original CT image will be lost. Besides, the 3D reconstruction from a optical thin section is not available because of the large size of the cutting slice. In this paper, we proposed an improved recurrent generative model to further enhance the reconstruction ability (512^{3}). Benefiting from the RNN-based architecture, the proposed model requires only one 3D training sample at least and generates the 3D structures layer by layer. There are three more improvements: First, a hybrid receptive field for the kernel of convolutional neural network is adopted. Second, an attention-based module is merged into the proposed model. Finally, a useful section loss is proposed to enhance the continuity along the Z direction. Three experiments are carried out to verify the effectiveness of the proposed model. Experimental results indicate the good reconstruction ability of proposed model in terms of accuracy, diversity, and generalization. And the effectiveness of section loss is also proved from the perspective of visual inspection and statistical comparison.

A Feature-Enriched Deep Convolutional Neural Network for JPEG Image Compression Artifacts Reduction and its Applications.

The amount of multimedia data, such as images and videos, has been increasing rapidly with the development of various imaging devices and the Internet, bringing more stress and challenges to information storage and transmission. The redundancy in images can be reduced to decrease data size via lossy compression, such as the most widely used standard Joint Photographic Experts Group (JPEG). However, the decompressed images generally suffer from various artifacts (e.g., blocking, banding, ringing, and blurring) due to the loss of information, especially at high compression ratios. This article presents a feature-enriched deep convolutional neural network for compression artifacts reduction (FeCarNet, for short). Taking the dense network as the backbone, FeCarNet enriches features to gain valuable information via introducing multi-scale dilated convolutions, along with the efficient 1 ×1 convolution for lowering both parameter complexity and computation cost. Meanwhile, to make full use of different levels of features in FeCarNet, a fusion block that consists of attention-based channel recalibration and dimension reduction is developed for local and global feature fusion. Furthermore, short and long residual connections both in the feature and pixel domains are combined to build a multi-level residual structure, thereby benefiting the network training and performance. In addition, aiming at reducing computation complexity further, pixel-shuffle-based image downsampling and upsampling layers are, respectively, arranged at the head and tail of the FeCarNet, which also enlarges the receptive field of the whole network. Experimental results show the superiority of FeCarNet over state-of-the-art compression artifacts reduction approaches in terms of both restoration capacity and model complexity. The applications of FeCarNet on several computer vision tasks, including image deblurring, edge detection, image segmentation, and object detection, demonstrate the effectiveness of FeCarNet further.

Diagnosis of Alzheimer's disease based on regional attention with sMRI gray matter slices.

BACKGROUND: Alzheimer's disease (AD) is the most common symptom of aggressive and irreversible dementia that affects people's ability of daily life. At present, neuroimaging technology plays an important role in the evaluation and early diagnosis of AD. With the widespread application of artificial intelligence in the medical field, deep learning has shown great potential in computer-aided AD diagnosis based on MRI. NEW METHOD: In this study, we proposed a deep learning framework based on sMRI gray matter slice for AD diagnosis. Compared with the previous methods based on deep learning, our method enhanced gray matter feature information more effectively by combination of slice region and attention mechanism, which can improve the accuracy on the AD diagnosis. RESULTS: To ensure the performance of our proposed method, the experiment was evaluated on T1 weighted structural MRI (sMRI) images with non-leakage splitting from the ADNI database. Our method can achieve 0.90 accuracy in classification of AD/NC and 0.825 accuracy in classification of AD/MCI, which has better diagnostic performance and advantages than other competitive single-modality methods based on sMRI. Furthermore, we indicated the most discriminative brain MRI slice area determined for AD diagnosis. COMPARISON WITH EXISTING METHODS: Our proposed method based on the regional attention with GM slice has a 1%-8% improvement in accuracy compared with several state-of-the-art methods for AD diagnosis. CONCLUSIONS: The results of experiment indicate that our method can focus more effective features in the gray matter of coronal slices and to achieve a more accurate diagnosis of Alzheimer's disease. This study can provide a more remarkably effective approach and more objective evaluation for the diagnosis of AD based on sMRI slice images.

Application of Machine Vision in Classifying Gait Frailty Among Older Adults.

Background: Frail older adults have an increased risk of adverse health outcomes and premature death. They also exhibit altered gait characteristics in comparison with healthy individuals. Methods: In this study, we created a Fried's frailty phenotype (FFP) labelled casual walking video set of older adults based on the West China Health and Aging Trend study. A series of hyperparameters in machine vision models were evaluated for body key point extraction (AlphaPose), silhouette segmentation (Pose2Seg, DPose2Seg, and Mask R-CNN), gait feature extraction (Gaitset, LGaitset, and DGaitset), and feature classification (AlexNet and VGG16), and were highly optimised during analysis of gait sequences of the current dataset. Results: The area under the curve (AUC) of the receiver operating characteristic (ROC) at the physical frailty state identification task for AlexNet was 0.851 (0.827-0.8747) and 0.901 (0.878-0.920) in macro and micro, respectively, and was 0.855 (0.834-0.877) and 0.905 (0.886-0.925) for VGG16 in macro and micro, respectively. Furthermore, this study presents the machine vision method equipped with better predictive performance globally than age and grip strength, as well as than 4-m-walking-time in healthy and pre-frailty classifying. Conclusion: The gait analysis method in this article is unreported and provides promising original tool for frailty and pre-frailty screening with the characteristics of convenience, objectivity, rapidity, and non-contact. These methods can be extended to any gait-related disease identification processes, as well as in-home health monitoring.

Three-dimensional reconstruction of porous media using super-dimension-based adjacent block-matching algorithm.

As porous media play an essential role in a variety of industrial applications, it is essential to understand their physical properties. Nowadays, the super-dimensional (SD) reconstruction algorithm is used to stochastically reconstruct a three-dimensional (3D) structure of porous media from a given two-dimensional image. This algorithm exhibits superiority in accuracy compared with classical algorithms because it learns information from the real 3D structure. However, owing to the short development time of the SD algorithm, it also has some limitations, such as inexact porosity characterization, long run time, blocking artifacts, and suboptimal accuracy that may be improved. To mitigate these limitations, this study presents the design of a special template that contains two parts of data (i.e., adjacent blocks and a central block); the proposed method matches adjacent blocks during reconstruction and assigns the matched central block to the area to be reconstructed. Furthermore, we design two important mechanisms during reconstruction: one for block matching and the other for porosity control. To verify the effectiveness of the proposed method compared with an existing SD method, both methods were tested on silica particle material and three homogeneous sandstones with different porosities; meanwhile, we compared the proposed method with a multipoint statistics method and a simulated annealing method. The reconstructed results were then compared with the target both visually and quantitatively. The experimental results indicate that the proposed method can overcome the aforementioned limitations and further improve the accuracy of existing methods. This method achieved 4-6 speedup factor compared with the traditional SD method.

Reconstruction of 3D greyscale image for reservoir rock from a single image based on pattern dictionary.

Most methods that model 3D porous media from 2D images are based on binary images. In this paper, we propose a method for reconstructing 3D greyscale isotropic porous media images from a single image. Our proposed method incorporates a fast-sampling procedure to control the continuity and variability between adjoining reconstruction layers, a new similarity calculation method to obtain the most similar patterns from a pattern dictionary, and a central area simulation procedure to solve the block effect problem. The reconstruction results from application of our proposed method to a real reservoir 3D model obtained via computed tomography (CT) and a comparison with the original CT structure demonstrate that our proposed method can reproduce properties such as autocorrelation function, linear function, shape distribution, average shape factor, average pore radius size, average throat radius size, average pore volume, permeability and grey histogram. Further, the comparison results indicate that the statistical characteristics of the reconstructions match the training image and the CT model perfectly.

Three-dimensional multiscale fusion for porous media on microtomography images of different resolutions.

Accurately acquiring the three-dimensional (3D) image of a porous medium is an imperative issue for the prediction of multiple physical properties. Considering the inherent nature of the multiscale pores contained in porous media such as tight sandstones, to completely characterize the pore structure, one needs to scan the microstructure at different resolutions. Specifically, low-resolution (LR) images cover a larger field of view (FOV) of the sample, but are lacking small-scale features, whereas high-resolution (HR) images contain ample information, but sometimes only cover a limited FOV. To address this issue, we propose a method for fusing the spatial information from a two-dimensional (2D) HR image into a 3D LR image, and finally reconstructing an integrated 3D structure with added fine-scale features. In the fusion process, the large-scale structure depicted by the 3D LR image is fixed as background and the 2D image is utilized as training image to reconstruct a small-scale structure based on the background. To assess the performance of our method, we test it on a sandstone scanned with low and high resolutions. Statistical properties between the reconstructed image and the target are quantitatively compared. The comparison indicates that the proposed method enables an accurate fusion of the LR and HR images because the small-scale information is precisely reproduced within the large one.

Multiscale modeling algorithm for core images.

Computed tomography (CT) images of large core samples acquired by imaging equipment are insufficiently clear and ineffectively describe the tiny pore structure; conversely, images of small core samples are insufficiently globally representative. To alleviate these challenges, the idea of a super-resolution reconstruction algorithm is combined with that of a three-dimensional core reconstruction algorithm, and a multiscale core CT image fusion reconstruction algorithm is proposed. To obtain sufficient image quality with high resolution, a large-scale core image is used to provide global feature information as well as information regarding the basic morphological structure of a large-scale pore and particle. Then the texture pattern and the tiny pore distribution information of a small-scale core image is used to refine the coarse large-scale core image. A blind image quality assessment is utilized to estimate the degradation model of core images at different scales. A multilevel pattern mapping dictionary containing local binary patterns is designed to speed up the pattern matching procedure, and an adaptive weighted reconstruction algorithm is designed to reduce the blockiness. With our method, images of the same core at different scales were successfully fused. The proposed algorithm is extensively tested on microstructures of different rock samples; all cases of the reconstructed results and those of the actual sample were found to be in good agreement with each other. The final reconstructed image contains both large-scale and small-scale information that can provide a better understanding of the core samples and inform the accurate calculation of parameters.

Super-resolution of real-world rock microcomputed tomography images using cycle-consistent generative adversarial networks.

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.

Reconstruction of porous media from extremely limited information using conditional generative adversarial networks.

Porous media are ubiquitous in both nature and engineering applications. Therefore, their modeling and understanding is of vital importance. In contrast to direct acquisition of three-dimensional (3D) images of this type of medium, obtaining its subregion (s) such as 2D images or several small areas can be feasible. Therefore, reconstructing whole images from limited information is a primary technique in these types of cases. Given data in practice cannot generally be determined by users and may be incomplete or only partially informed, thus making existing reconstruction methods inaccurate or even ineffective. To overcome this shortcoming, in this study we propose a deep-learning-based framework for reconstructing full images from their much smaller subareas. In particular, conditional generative adversarial network is utilized to learn the mapping between the input (a partial image) and output (a full image). To ensure 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. Because of the inherent essence of this ill-posed problem, a Gaussian noise is introduced for producing reconstruction diversity, thus enabling the network to provide multiple candidate outputs. Our method is extensively tested on a variety of porous materials and validated by both visual inspection and quantitative comparison. It is shown to be accurate, stable, and even fast (∼0.08 s for a 128×128 image reconstruction). The proposed approach can be readily extended by, for example, incorporating user-defined conditional data and an arbitrary number of object functions into reconstruction, while being coupled with other reconstruction methods.

Dictionary optimization and constraint neighbor embedding-based dictionary mapping for superdimension reconstruction of porous media.

The three-dimensional (3D) structure of a digital core can be reconstructed from a single two-dimensional (2D) image via mathematical modeling. In classical mathematical modeling algorithms, such as multipoint geostatistics algorithms, the optimization of pattern sets (dictionaries) and the mapping problems are important issues. However, they have rarely been discussed thus far. Pattern set (dictionary)-related problems include the pattern set (dictionary) size problem and the one-to-many mapping problem in a pattern set (dictionary). The former directly affects the completeness of the dictionary, while the latter is manifested such that a single to-be-matched 2D patch has multiple matching patterns in the library and it is hence necessary to select these modes to establish an optimal mapping relationship. Whether the two above-mentioned problems can be properly resolved is directly related to the accuracy of the reconstruction results. Super-dimension reconstruction is a new 3D reconstruction method proposed by introducing the concepts of training dictionary, prior model, and mapping into the reconstruction of the digital core from the field of super-resolution reconstruction. In addition, mapping relationship extraction and dictionary building are also key issues in super-dimension reconstruction. Therefore, this paper discusses these common dictionary-related problems from the perspective of super-dimension dictionaries. We propose dictionary optimization using augmentation dictionaries and clustering based on the boundary features of the dictionary elements to improve the completeness and expand the expression ability of the dictionary. Furthermore, we propose constraint neighbor embedding-based dictionary mapping to establish a more reasonable dictionary mapping relationship for super-dimension reconstruction, and we solve the one-to-many mapping problem in the dictionary. Our experimental results show that the performance of the super-dimension dictionary can be improved by the above-mentioned algorithm. Thus, through the optimized dictionary structure and mapping relationship determined by the above-mentioned methods, the 2D patch to be reconstructed can match a more accurate 3D block in the dictionary. Consequently, the reconstruction precision is improved.

Improved multipoint statistics method for reconstructing three-dimensional porous media from a two-dimensional image via porosity matching.

Reconstructing a three-dimensional (3D) structure from a single two-dimensional training image (TI) is a challenging issue. Multiple-point statistics (MPS) is an effective method to solve this problem. However, in the traditional MPS method, errors occur while statistical features of reconstruction, such as porosity, connectivity, and structural properties, deviate from those of TI. Due to the MPS reconstruction mechanism that the voxel being reconstructed is dependent on the reconstructed voxel, it may cause error accumulation during simulations, which can easily lead to a significant difference between the real 3D structure and the reconstructed result. To reduce error accumulation and improve morphological similarity, an improved MPS method based on porosity matching is proposed. In the reconstruction, we search the matching pattern in the TI directly. Meanwhile, a multigrid approach is also applied to capture the large-scale structures of the TI. To demonstrate its superiority over the traditional MPS method, our method is tested on different sandstone samples from many aspects, including accuracy, stability, generalization, and flow characteristics. Experimental results show that the reconstruction results by the improved MPS method effectively match the CT sandstone samples in correlation functions, local porosity distribution, morphological parameters, and permeability.

Markov prior-based block-matching algorithm for superdimension reconstruction of porous media.

A superdimension reconstruction algorithm is used for the reconstruction of three-dimensional (3D) structures of a porous medium based on a single two-dimensional image. The algorithm borrows the concepts of "blocks," "learning," and "dictionary" from learning-based superresolution reconstruction and applies them to the 3D reconstruction of a porous medium. In the neighborhood-matching process of the conventional superdimension reconstruction algorithm, the Euclidean distance is used as a criterion, although it may not really reflect the structural correlation between adjacent blocks in an actual situation. Hence, in this study, regular items are adopted as prior knowledge in the reconstruction process, and a Markov prior-based block-matching algorithm for superdimension reconstruction is developed for more accurate reconstruction. The algorithm simultaneously takes into consideration the probabilistic relationship between the already reconstructed blocks in three different perpendicular directions (x, y, and z) and the block to be reconstructed, and the maximum value of the probability product of the blocks to be reconstructed (as found in the dictionary for the three directions) is adopted as the basis for the final block selection. Using this approach, the problem of an imprecise spatial structure caused by a point simulation can be overcome. The problem of artifacts in the reconstructed structure is also addressed through the addition of hard data and by neighborhood matching. To verify the improved reconstruction accuracy of the proposed method, the statistical and morphological features of the results from the proposed method and traditional superdimension reconstruction method are compared with those of the target system. The proposed superdimension reconstruction algorithm is confirmed to enable a more accurate reconstruction of the target system while also eliminating artifacts.

Evaluating the morphological completeness of a training image.

Understanding the three-dimensional (3D) stochastic structure of a porous medium is helpful for studying its physical properties. A 3D stochastic structure can be reconstructed from a two-dimensional (2D) training image (TI) using mathematical modeling. In order to predict what specific morphology belonging to a TI can be reconstructed at the 3D orthogonal slices by the method of 3D reconstruction, this paper begins by introducing the concept of orthogonal chords. After analyzing the relationship among TI morphology, orthogonal chords, and the 3D morphology of orthogonal slices, a theory for evaluating the morphological completeness of a TI is proposed for the cases of three orthogonal slices and of two orthogonal slices. The proposed theory is evaluated using four TIs of porous media that represent typical but distinct morphological types. The significance of this theoretical evaluation lies in two aspects: It allows special morphologies, for which the attributes of a TI can be reconstructed at a special orthogonal slice of a 3D structure, to be located and quantified, and it can guide the selection of an appropriate reconstruction method for a special TI.

Single Image Super-Resolution Using Local Geometric Duality and Non-Local Similarity.

Super-resolution (SR) from a single image plays an important role in many computer vision applications. It aims to estimate a high-resolution (HR) image from an input low- resolution (LR) image. To ensure a reliable and robust estimation of the HR image, we propose a novel single image SR method that exploits both the local geometric duality (GD) and the non-local similarity of images. The main principle is to formulate these two typically existing features of images as effective priors to constrain the super-resolved results. In consideration of this principle, the robust soft-decision interpolation method is generalized as an outstanding adaptive GD (AGD)-based local prior. To adaptively design weights for the AGD prior, a local non-smoothness detection method and a directional standard-deviation-based weights selection method are proposed. After that, the AGD prior is combined with a variational-framework-based non-local prior. Furthermore, the proposed algorithm is speeded up by a fast GD matrices construction method, which primarily relies on the selective pixel processing. The extensive experimental results verify the effectiveness of the proposed method compared with several state-of-the-art SR algorithms.

Pattern density function for reconstruction of three-dimensional porous media from a single two-dimensional image.

Three-dimensional (3D) structures are useful for studying the spatial structures and physical properties of porous media. A 3D structure can be reconstructed from a single two-dimensional (2D) training image (TI) by using mathematical modeling methods. Among many reconstruction algorithms, an optimal-based algorithm was developed and has strong stability. However, this type of algorithm generally uses an autocorrelation function (which is unable to accurately describe the morphological features of porous media) as its objective function. This has negatively affected further research on porous media. To accurately reconstruct 3D porous media, a pattern density function is proposed in this paper, which is based on a random variable employed to characterize image patterns. In addition, the paper proposes an original optimal-based algorithm called the pattern density function simulation; this algorithm uses a pattern density function as its objective function, and adopts a multiple-grid system. Meanwhile, to address the key point of algorithm reconstruction speed, we propose the use of neighborhood statistics, the adjacent grid and reversed phase method, and a simplified temperature-controlled mechanism. The pattern density function is a high-order statistical function; thus, when all grids in the reconstruction results converge in the objective functions, the morphological features and statistical properties of the reconstruction results will be consistent with those of the TI. The experiments include 2D reconstruction using one artificial structure, and 3D reconstruction using battery materials and cores. Hierarchical simulated annealing and single normal equation simulation are employed as the comparison algorithms. The autocorrelation function, linear path function, and pore network model are used as the quantitative measures. Comprehensive tests show that 3D porous media can be reconstructed accurately from a single 2D training image by using the method proposed in this paper.