Privacy-enhancing methodologies and privacy risk discovery in neuroimaging data: From differentially private distribution estimation and visualization to brain foundation model evaluation

Privacy protection has become increasingly important in data science and is especially critical in neuroimaging, where limited data at individual sites often motivates multi-site collaboration. Sharing data in such settings typically involves cumbersome and time-consuming approval procedures. Differential privacy (DP) provides a systematic framework for data sharing while balancing privacy and utility. In this dissertation, we introduce novel methods for distribution approximation and visualization under differential privacy. We also investigate the use of large-scale pre-trained models to obtain compact representations of fMRI data, assessing both their utility for downstream analyses and the risk of exposing batch information. We first focus on privacy-preserving distribution approximation. The cumulative distribution function (CDF) is fundamental for characterizing random variables, making it a key tool in privacy-preserving analysis. We introduce a novel framework for constructing differentially private CDFs inspired by functional analysis and the functional mechanism. Two variants are developed: a polynomial projection method, which projects the empirical CDF into a polynomial space, and a sparse approximation method via matching pursuit, which projects it into arbitrary function spaces constructed from dictionaries. In both cases, the empirical CDF is approximated within the chosen space, and the corresponding coefficients are privatized to guarantee differential privacy. Compared with existing approaches such as histogram queries and adaptive quantiles, our methods achieve comparable or superior performance. They are particularly well-suited to decentralized settings and scenarios where CDFs must be efficiently updated with newly collected or streaming data. We also investigate the impact of parameters such as dictionary size and systematically evaluate different dictionary constructions, including Legendre polynomials, B-splines, and distribution-based functions. Beyond protecting data, visualizations can themselves reveal sensitive information; for example, individual values can be inferred directly from boxplots or scatterplots. Privacy-preserving visualizations can be categorized into two types. The first type relies on synthetic data generated from differentially private distribution approximation, which allows downstream analyses without accessing raw data. However, producing accurate approximations is particularly challenging in high-dimensional settings. The second type applies privacy-preserving techniques directly to visual representations derived from the data. While existing differential privacy methods are well-established for numerical data, it remains unclear whether they can be directly adapted to visual representations, as preserving the information conveyed by the original visualization may require different considerations. This motivates our investigation of DP visualization techniques. We focus on neuroimaging analyses of functional network connectivity (FNC), exploring several perturbation-based approaches to correlation values and characterizing their privacy costs as well as pre- and post-processing impacts. To improve the tradeoff between privacy and visual utility, we propose workflows for connectogram and seed-based connectivity visualizations, which produce results similar to their non-private counterparts. Experimental results demonstrate that these methods preserve the information conveyed by the original visualization while ensuring privacy, highlighting the potential of differential privacy for secure and informative visual analytics. We also investigate the use of large-scale pre-trained models to obtain compact embeddings of functional magnetic resonance imaging (fMRI) data, which may facilitate multi-site analyses without exchanging high-dimensional raw scans. Using embeddings generated by BrainLM and SwiFT across multiple datasets, including FBIRN, ADHD-200, and ABIDE I, we evaluate their properties using both qualitative methods such as PCA and LDA and quantitative approaches including PERMANOVA and classification models for site and diagnostic labels. Our results indicate that while these embeddings encode clinically relevant signals, they are strongly influenced by batch effects, which can dominate over subtle diagnostic information and reveal batch membership. Ridge regression analyses predicting brain measures such as ALFF and FNC further show that BrainLM embeddings are particularly sensitive to regional activity, whereas SwiFT embeddings preferentially capture functional connectivity patterns. These findings illustrate the dual nature of foundation model embeddings: they provide powerful, compact representations that capture meaningful brain information while simultaneously carrying non-negligible signals that could expose batch characteristics. To summarize, this dissertation presents privacy-aware neuroimaging analyses in three complementary directions. We develop novel and efficient differentially private methods for distribution approximation. We design differentially private visualization techniques that preserve the information conveyed by the original visualizations while controlling privacy risks. Finally, we evaluate large-scale pre-trained foundation models, showing that compact embeddings can capture meaningful brain information, but they can also unintentionally reveal batch membership.