In today's data-driven world, privacy is a significant concern. It is crucial to preserve the privacy of sensitive information while visualizing data. This thesis aims to develop new techniques and software tools that support Vega-Lite visualizations while maintaining privacy. Vega-Lite is a visualization grammar based on Wilkinson's grammar of graphics. The project extends Vega-Lite to incorporate privacy algorithms such as k-anonymity, l-diversity, t-closeness, and differential privacy. This is done by using a unique multi-input loop module logic that generates combinations of attributes as a new anonymization method. Differential privacy is implemented by adding controlled noise (Laplace or Exponential) to the sensitive columns in the dataset. The user defines custom rules in the JSON schema, mentioning the privacy methods and the sensitive column. The schema is validated using Another JSON Validation library, and these rules help identify the anonymization techniques to be performed on the dataset before sending it back to the Vega-Lite visualization server. Multiple datasets satisfying the privacy requirements are generated, and their utility scores are provided so that the user can trade-off between privacy and utility on the datasets based on their requirements. The interface developed is user-friendly and intuitive and guides users in using it. It provides appropriate feedback on the privacy-preserving visualizations generated through various utility metrics. This application is helpful for technical or domain experts across multiple domains where privacy is a big concern, such as medical institutions, traffic and urban planning, financial institutions, educational records, and employer-employee relations. This project is novel as it provides a one-stop solution for privacy-preserving visualization. It works on open-source software, Vega-Lite, which several organizations and users use for business and educational purposes.

As robots become increasingly integrated into the environments, they need to learn how to interact with the objects around them. Many of these objects are articulated with multiple degrees of freedom (DoF). Multi-DoF objects have complex joints that require specific manipulation orders, but existing methods only consider objects with a single joint. To capture the joint structure and manipulation sequence of any object, I introduce the "Object Kinematic State Machines" (OKSMs), a novel representation that models the kinematic constraints and manipulation sequences of multi-DoF objects. I also present Pokenet, a deep neural network architecture that estimates the OKSMs from the sequence of point cloud data of human demonstrations. I conduct experiments on both simulated and real-world datasets to validate my approach. First, I evaluate the modeling of multi-DoF objects on a simulated dataset, comparing against the current state-of-the-art method. I then assess Pokenet's real-world usability on a dataset collected in my lab, comprising 5,500 data points across 4 objects. Results showcase that my method can successfully estimate joint parameters of novel multi-DoF objects with over 25% more accuracy on average than prior methods.

Image denoising, a fundamental task in computer vision, poses significant challenges due to its inherently inverse and ill-posed nature. Despite advancements in traditional methods and supervised learning approaches, particularly in medical imaging such as Medical Resonance Imaging (MRI) scans, the reliance on paired datasets and known noise distributions remains a practical hurdle. Recent progress in noise statistical independence theory and diffusion models has revitalized research interest, offering promising avenues for unsupervised denoising. However, existing methods often yield overly smoothed results or introduce hallucinated structures, limiting their clinical applicability. This thesis tackles the core challenge of progressing towards unsupervised denoising of MRI scans. It aims to retain intricate details without smoothing or introducing artificial structures, thus ensuring the production of high-quality MRI images. The thesis makes a three-fold contribution: Firstly, it presents a detailed analysis of traditional techniques, early machine learning algorithms for denoising, and new statistical-based models, with an extensive evaluation study on self-supervised denoising methods highlighting their limitations. Secondly, it conducts an evaluation study on an emerging class of diffusion-based denoising methods, accompanied by additional empirical findings and discussions on their effectiveness and limitations, proposing solutions to enhance their utility. Lastly, it introduces a novel approach, Unsupervised Multi-stage Ensemble Deep Learning with diffusion models for denoising MRI scans (MEDL). Leveraging diffusion models, this approach operates independently of signal or noise priors and incorporates weighted rescaling of multi-stage reconstructions to balance over-smoothing and hallucination tendencies. Evaluation using benchmark datasets demonstrates an average gain of 1dB and 2% in PSNR and SSIM metrics, respectively, over existing approaches.

Structural Magnetic Resonance Imaging analysis is a vital component in the study of Alzheimer’s Disease pathology and several techniques exist as part of the existing research conducted. In particular, volumetric approaches in this field are known to be beneficial due to the increased capability to express morphological characteristics when compared to manifold methods. To aid in the improvement of the field, this paper aims to propose an intrinsic volumetric conic system that can be applied to bounded volumetric meshes to enable a more effective study of subjects. The computation of the metric involves the use of heat kernel theory and conformal parameterization on genus-0 surfaces extended to a volumetric domain. Additionally, this paper also explores the use of the ’TetCNN’ architecture on the classification of hippocampal tetrahedral meshes to detect features that correspond to Alzheimer’s indicators. The model tested was able to achieve remarkable results with a measured classification accuracy of above 90% in the task of differentiating between subjects diagnosed with Alzheimer’s and normal control subjects.

Neural tissue is a delicate system comprised of neurons and their synapses, glial cells for support, and vasculature for oxygen and nutrient delivery. This complexity ultimately gives rise to the human brain, a system researchers have become increasingly interested in replicating for artificial intelligence purposes. Some have even gone so far as to use neuronal cultures as computing hardware, but utilizing an environment closer to a living brain means having to grapple with the same issues faced by clinicians and researchers trying to treat brain disorders. Most outstanding among these are the problems that arise with invasive interfaces. Optical techniques that use fluorescent dyes and proteins have emerged as a solution for noninvasive imaging with single-cell resolution in vitro and in vivo, but feeding in information in the form of neuromodulation still requires implanted electrodes. The implantation process of these electrodes damages nearby neurons and their connections, causes hemorrhaging, and leads to scarring and gliosis that diminish efficacy. Here, a new approach for noninvasive neuromodulation with high spatial precision is described. It makes use of a combination of ultrasound, high frequency acoustic energy that can be focused to submillimeter regions at significant depths, and electric fields, an effective tool for neuromodulation that lacks spatial precision when used in a noninvasive manner. The hypothesis is that, when combined in a specific manner, these will lead to nonlinear effects at neuronal membranes that cause cells only in the region of overlap to be stimulated. Computational modeling confirmed this combination to be uniquely stimulating, contingent on certain physical effects of ultrasound on cell membranes. Subsequent in vitro experiments led to inconclusive results, however, leaving the door open for future experimentation with modified configurations and approaches. The specific combination explored here is also not the only untested technique that may achieve a similar goal.

Beta-Amyloid(Aβ) plaques and tau protein tangles in the brain are now widely recognized as the defining hallmarks of Alzheimer’s disease (AD), followed by structural atrophy detectable on brain magnetic resonance imaging (MRI) scans. However, current methods to detect Aβ/tau pathology are either invasive (lumbar puncture) or quite costly and not widely available (positron emission tomography (PET)). And one of the particular neurodegenerative regions is the hippocampus to which the influence of Aβ/tau on has been one of the research projects focuses in the AD pathophysiological progress. In this dissertation, I proposed three novel machine learning and statistical models to examine subtle aspects of the hippocampal morphometry from MRI that are associated with Aβ /tau burden in the brain, measured using PET images. The first model is a novel unsupervised feature reduction model to generate a low-dimensional representation of hippocampal morphometry for each individual subject, which has superior performance in predicting Aβ/tau burden in the brain. The second one is an efficient federated group lasso model to identify the hippocampal subregions where atrophy is strongly associated with abnormal Aβ/Tau. The last one is a federated model for imaging genetics, which can identify genetic and transcriptomic influences on hippocampal morphometry. Finally, I stated the results of these three models that have been published or submitted to peer-reviewed conferences and journals.

This dissertation constructs a new computational processing framework to robustly and precisely quantify retinotopic maps based on their angle distortion properties. More generally, this framework solves the problem of how to robustly and precisely quantify (angle) distortions of noisy or incomplete (boundary enclosed) 2-dimensional surface to surface mappings. This framework builds upon the Beltrami Coefficient (BC) description of quasiconformal mappings that directly quantifies local mapping (circles to ellipses) distortions between diffeomorphisms of boundary enclosed plane domains homeomorphic to the unit disk. A new map called the Beltrami Coefficient Map (BCM) was constructed to describe distortions in retinotopic maps. The BCM can be used to fully reconstruct the original target surface (retinal visual field) of retinotopic maps. This dissertation also compared retinotopic maps in the visual processing cascade, which is a series of connected retinotopic maps responsible for visual data processing of physical images captured by the eyes. By comparing the BCM results from a large Human Connectome project (HCP) retinotopic dataset (N=181), a new computational quasiconformal mapping description of the transformed retinal image as it passes through the cascade is proposed, which is not present in any current literature. The description applied on HCP data provided direct visible and quantifiable geometric properties of the cascade in a way that has not been observed before. Because retinotopic maps are generated from in vivo noisy functional magnetic resonance imaging (fMRI), quantifying them comes with a certain degree of uncertainty. To quantify the uncertainties in the quantification results, it is necessary to generate statistical models of retinotopic maps from their BCMs and raw fMRI signals. Considering that estimating retinotopic maps from real noisy fMRI time series data using the population receptive field (pRF) model is a time consuming process, a convolutional neural network (CNN) was constructed and trained to predict pRF model parameters from real noisy fMRI data

Little is known about how cognitive and brain aging patterns differ in older adults with autism spectrum disorder (ASD). However, recent evidence suggests that individuals with ASD may be at greater risk of pathological aging conditions than their neurotypical (NT) counterparts. A growing body of research indicates that older adults with ASD may experience accelerated cognitive decline and neurodegeneration as they age, although studies are limited by their cross-sectional design in a population with strong age-cohort effects. Studying aging in ASD and identifying biomarkers to predict atypical aging is important because the population of older individuals with ASD is growing. Understanding the unique challenges faced as autistic adults age is necessary to develop treatments to improve quality of life and preserve independence. In this study, a longitudinal design was used to characterize cognitive and brain aging trajectories in ASD as a function of autistic trait severity. Principal components analysis (PCA) was used to derive a cognitive metric that best explains performance variability on tasks measuring memory ability and executive function. The slope of the integrated persistent feature (SIP) was used to quantify functional connectivity; the SIP is a novel, threshold-free graph theory metric which summarizes the speed of information diffusion in the brain. Longitudinal mixed models were using to predict cognitive and brain aging trajectories (measured via the SIP) as a function of autistic trait severity, sex, and their interaction. The sensitivity of the SIP was also compared with traditional graph theory metrics. It was hypothesized that older adults with ASD would experience accelerated cognitive and brain aging and furthermore, age-related changes in brain network topology would predict age-related changes in cognitive performance. For both cognitive and brain aging, autistic traits and sex interacted to predict trajectories, such that older men with high autistic traits were most at risk for poorer outcomes. In men with autism, variability in SIP scores across time points trended toward predicting cognitive aging trajectories. Findings also suggested that autistic traits are more sensitive to differences in brain aging than diagnostic group and that the SIP is more sensitive to brain aging trajectories than other graph theory metrics. However, further research is required to determine how physiological biomarkers such as the SIP are associated with cognitive outcomes.

Alzheimer's disease (AD) is a neurodegenerative disease that damages the cognitive abilities of a patient. It is critical to diagnose AD early to begin treatment as soon as possible which can be done through biomarkers. One such biomarker is the beta-amyloid (Aβ) peptide which can be quantified using the centiloid (CL) scale. For identifying the Aβ biomarker, A deep learning model that can model AD progression by predicting the CL value for brain magnetic resonance images (MRIs) is proposed. Brain MRI images can be obtained through the Alzheimer's Disease Neuroimaging Initiative (ADNI) and Open Access Series of Imaging Studies (OASIS) datasets, however a single model cannot perform well on both datasets at once. Thus, A regularization-based continuous learning framework to perform domain adaptation on the previous model is also proposed which captures the latent information about the relationship between Aβ and AD progression within both datasets.

Retinotopic map, the map between visual inputs on the retina and neuronal activation in brain visual areas, is one of the central topics in visual neuroscience. For human observers, the map is typically obtained by analyzing functional magnetic resonance imaging (fMRI) signals of cortical responses to slowly moving visual stimuli on the retina. Biological evidences show the retinotopic mapping is topology-preserving/topological (i.e. keep the neighboring relationship after human brain process) within each visual region. Unfortunately, due to limited spatial resolution and the signal-noise ratio of fMRI, state of art retinotopic map is not topological. The topic was to model the topology-preserving condition mathematically, fix non-topological retinotopic map with numerical methods, and improve the quality of retinotopic maps. The impose of topological condition, benefits several applications. With the topological retinotopic maps, one may have a better insight on human retinotopic maps, including better cortical magnification factor quantification, more precise description of retinotopic maps, and potentially better exam ways of in Ophthalmology clinic.