Section on Statistics in Imaging Student Paper Award Winners

Regression models are widely used in neuroimaging studies to learn complex associations between clinical variables and image data. Gaussian process (GP) is one of the most popular Bayesian nonparametric methods and has been widely used as prior models for the unknown functions in those models. However, many existing GP methods need to pre-specify the functional form of the kernels, which often suffer less flexibility in model fitting and computational bottlenecks in large-scale datasets. To address these challenges, we develop a scalable Bayesian kernel learning framework for GP priors in various image regression models. Our approach leverages deep neural networks (DNNs) to perform low-rank approximations of GP kernel functions via spectral decomposition. With Bayesian kernel learning techniques, we achieve improved accuracy in parameter estimation and variable selection in image regression models. We establish large prior support and posterior consistency of the kernel estimations. Through extensive simulations, we demonstrate our model outperforms other competitive methods. We illustrate the proposed method by analyzing multiple neuroimaging datasets in different medical studies. 

Voxel-based multiple testing is widely used in neuroimaging data analysis. Traditional false discovery rate (FDR) control methods often ignore the spatial dependence among the voxel-based tests and thus suffer from substantial loss of testing power. While recent spatial FDR control methods have emerged, their validity and optimality remain questionable when handling the complex spatial dependencies of the brain. Concurrently, deep learning methods have revolutionized image segmentation, a task closely related to voxel-based multiple testing. In this paper, we propose DeepFDR, a novel spatial FDR control method that leverages unsupervised deep learning-based image segmentation to address the voxel-based multiple testing problem. Numerical studies, including comprehensive simulations and Alzheimer's disease FDG-PET image analysis, demonstrate DeepFDR's superiority over existing methods. DeepFDR not only excels in FDR control and effectively diminishes the false nondiscovery rate, but also boasts exceptional computational efficiency highly suited for tackling large-scale neuroimaging data. 

In brain research, joint analysis of multimodal neuroimaging data is vital for understanding complex brain structure-function interactions. We examine the influence of structural imaging (SI) features, such as white matter integrity and cortical thickness, on the functional connectome network. Our network-based matrix-on-vector regression model delineates FC-SI association patterns. We introduce a multi-level dense bipartite and clique subgraph extraction algorithm, pinpointing spatially specific SI features that significantly influence FC sub-networks. This method identifies correlated structural-connectomic patterns and minimizes false positives in analyzing millions of interactions. Applied to 4,242 UK Biobank participants, our method assesses the impact of whole-brain white matter integrity and cortical thickness on resting-state functional connectome. Findings show significant influences of white matter on corticospinal tracts and inferior cerebellar peduncle on sensorimotor, salience, and executive networks, with an average correlation of 0.81 (p<0.001). 

Independent component analysis (ICA) is widely used to estimate spatial resting-state networks and their time courses in neuroimaging studies. Independent components correspond to sparse patterns of co-activating brain locations. Previous approaches for introducing sparsity to ICA replace the non-smooth objective function with smooth approximations, resulting in components that do not achieve exact zeros. We propose a novel Sparse ICA method that enables sparse estimation of independent source components by solving a non-smooth non-convex optimization problem via the relax-and-split framework. The proposed Sparse ICA method balances statistical independence and sparsity simultaneously and is computationally fast. In simulations, we demonstrate improved estimation accuracy of both source signals and signal time courses compared to existing approaches. We apply Sparse ICA to cortical surface resting-state fMRI in school-aged autistic children, and reveal differences in brain activity between certain regions in autistic children compared to normal children. Sparse ICA selects co-activating locations, which we argue is more interpretable than dense components from popular approaches. 

Identifying the boundaries of irregular regions of extended astronomical emission poses significant challenges due to their complex features and background contamination. In high-energy astrophysics, one strategy is to segment event lists by using algorithms that aggregate photons into distinct spatial clusters, typically based on their two-dimensional sky coordinates. \citet{Fan_2023}, for example, introduced ``Seeded Region Growing on a Graph'' (\srgong), which combines a likeihood-based representation of an inhomogenious Poisson process with flexible non-parametric representation of the segments to derive maximum likelihood estimates of the segments, their number, and their Poisson rates. In this paper, we first introduce several modifications to \srgong\ to enhance its performance and stability under low Signal-to-Noise (S/N) conditions. In addition, we introduce \uqbose, a new set of algorithms and statistical methods that quantify the uncertainty associated with a segment boundary. This is accomplished via a parameterization of the boundary derived using Fourier Descriptors along with spatial bootstrap techniques, including both parametric and non-parametric methods, to effectively assess the uncertainty of the parameter estimates. We also construct a small-size global confidence region for the true object shape and validate the overall \uqbose\ procedure through comparisons between the empirical coverage rate of the global confidence region with its theoretical bounds under various numerical experiment scenarios.