Applications of Physically Accurate Deep Learning for Processing Digital Rock Images

Digital rock analysis aims to improve our understanding of the fluid flow properties of reservoir rocks, which are important for enhanced oil recovery, hydrogen storage, carbonate dioxide storage, and groundwater management. X-ray microcomputed tomography (micro-CT) is the primary approach to capturing the structure of porous rock samples for digital rock analysis. Initially, the obtained micro-CT images are processed using image-based techniques, such as registration, denoising, and segmentation depending on various requirements. Numerical simulations are then conducted on the digital models for petrophysical prediction. The accuracy of the numerical simulation highly depends on the quality of the micro-CT images. Therefore, image processing is a critical step for digital rock analysis. Recent advances in deep learning have surpassed conventional methods for image processing. Herein, the utility of convolutional neural networks (CNN) and generative adversarial networks (GAN) are assessed in regard to various applications in digital rock image processing, such as segmentation, super-resolution, and denoising. To obtain training data, different sandstone and carbonate samples were scanned using various micro-CT facilities. After that, validation images previously unseen by the trained neural networks are utilised to evaluate the performance and robustness of the proposed deep learning techniques. Various threshold scenarios are applied to segment the reconstructed digital rock images for sensitivity analyses. Then, quantitative petrophysical analyses, such as porosity, absolute/relative permeability, and pore size distribution, are implemented to estimate the physical accuracy of the digital rock data with the corresponding ground truth data. The results show that both CNN and GAN deep learning methods can provide physically accurate digital rock images with less user bias than traditional approaches. These results unlock new pathways for various applications related to the reservoir characterisation of porous reservoir rocks

Deep learning-based diagnostic system for malignant liver detection

Cancer is the second most common cause of death of human beings, whereas liver cancer is the fifth most common cause of mortality. The prevention of deadly diseases in living beings requires timely, independent, accurate, and robust detection of ailment by a computer-aided diagnostic (CAD) system. Executing such intelligent CAD requires some preliminary steps, including preprocessing, attribute analysis, and identification. In recent studies, conventional techniques have been used to develop computer-aided diagnosis algorithms. However, such traditional methods could immensely affect the structural properties of processed images with inconsistent performance due to variable shape and size of region-of-interest. Moreover, the unavailability of sufficient datasets makes the performance of the proposed methods doubtful for commercial use. To address these limitations, I propose novel methodologies in this dissertation. First, I modified a generative adversarial network to perform deblurring and contrast adjustment on computed tomography (CT) scans. Second, I designed a deep neural network with a novel loss function for fully automatic precise segmentation of liver and lesions from CT scans. Third, I developed a multi-modal deep neural network to integrate pathological data with imaging data to perform computer-aided diagnosis for malignant liver detection. The dissertation starts with background information that discusses the proposed study objectives and the workflow. Afterward, Chapter 2 reviews a general schematic for developing a computer-aided algorithm, including image acquisition techniques, preprocessing steps, feature extraction approaches, and machine learning-based prediction methods. The first study proposed in Chapter 3 discusses blurred images and their possible effects on classification. A novel multi-scale GAN network with residual image learning is proposed to deblur images. The second method in Chapter 4 addresses the issue of low-contrast CT scan images. A multi-level GAN is utilized to enhance images with well-contrast regions. Thus, the enhanced images improve the cancer diagnosis performance. Chapter 5 proposes a deep neural network for the segmentation of liver and lesions from abdominal CT scan images. A modified Unet with a novel loss function can precisely segment minute lesions. Similarly, Chapter 6 introduces a multi-modal approach for liver cancer variants diagnosis. The pathological data are integrated with CT scan images to diagnose liver cancer variants. In summary, this dissertation presents novel algorithms for preprocessing and disease detection. Furthermore, the comparative analysis validates the effectiveness of proposed methods in computer-aided diagnosis

Metric and Representation Learning

All data has some inherent mathematical structure. I am interested in understanding the intrinsic geometric and probabilistic structure of data to design effective algorithms and tools that can be applied to machine learning and across all branches of science. The focus of this thesis is to increase the effectiveness of machine learning techniques by developing a mathematical and algorithmic framework using which, given any type of data, we can learn an optimal representation. Representation learning is done for many reasons. It could be done to fix the corruption given corrupted data or to learn a low dimensional or simpler representation, given high dimensional data or a very complex representation of the data. It could also be that the current representation of the data does not capture the important geometric features of the data. One of the many challenges in representation learning is determining ways to judge the quality of the representation learned. In many cases, the consensus is that if d is the natural metric on the representation, then this metric should provide meaningful information about the data. Many examples of this can be seen in areas such as metric learning, manifold learning, and graph embedding. However, most algorithms that solve these problems learn a representation in a metric space first and then extract a metric. A large part of my research is exploring what happens if the order is switched, that is, learn the appropriate metric first and the embedding later. The philosophy behind this approach is that understanding the inherent geometry of the data is the most crucial part of representation learning. Often, studying the properties of the appropriate metric on the input data sets indicates the type of space, we should be seeking for the representation. Hence giving us more robust representations. Optimizing for the appropriate metric can also help overcome issues such as missing and noisy data. My projects fall into three different areas of representation learning. 1) Geometric and probabilistic analysis of representation learning methods. 2) Developing methods to learn optimal metrics on large datasets. 3) Applications. For the category of geometric and probabilistic analysis of representation learning methods, we have three projects. First, designing optimal training data for denoising autoencoders. Second, formulating a new optimal transport problem and understanding the geometric structure. Third, analyzing the robustness to perturbations of the solutions obtained from the classical multidimensional scaling algorithm versus that of the true solutions to the multidimensional scaling problem. For learning optimal metric, we are given a dissimilarity matrix $hat{D}$, some function $f$ and some a subset $S$ of the space of all metrics and we want to find $D in S$ that minimizes $f(D,hat{D})$. In this thesis, we consider the version of the problem when $S$ is the space of metrics defined on a fixed graph. That is, given a graph $G$, we let $S$, be the space of all metrics defined via $G$. For this $S$, we consider the sparse objective function as well as convex objective functions. We also looked at the problem where we want to learn a tree. We also show how the ideas behind learning the optimal metric can be applied to dimensionality reduction in the presence of missing data. Finally, we look at an application to real world data. Specifically trying to reconstruct ancient Greek text.PHDApplied and Interdisciplinary MathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/169738/1/rsonthal_1.pd