Tensor and Subspace Learning Methods with Applications to Medical Imaging

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Medical imaging techniques have become increasingly important for both clinical and research studies. For example, cone beam computed tomography has a major role in diagnosis and treatment planning in dentistry, and functional magnetic resonance imaging is routinely used to help researchers characterize brain activity. More efficient and powerful statistical techniques are needed to analyze medical imaging for diagnosis and prediction of diseases and other disorders. Through this project, new statistical theory, methods, and algorithms will be developed for the analysis of large complex data such as medical imaging data sets. The research is expected to provide new theoretical insights and practical methodologies that advance multivariate statistics while simultaneously responding to the growing needs and challenges of medical imaging data analysis. Results of the research in this project will be disseminated through collaborations with neuroscientists and biomedical engineers, as well as substantial graduate student training and outreach activities. Open source and user-friendly software will also be produced.Ultra-high dimensionality, tensor structure, and high correlations are embedded in modern scientific and engineering data. Estimation and inferential techniques become inefficient or even inconsistent if they ignore high correlations among variables, heterogeneity caused by additional covariates, or intrinsic structural information. To address these challenges, statistically rigorous and computationally efficient learning methods will be developed. A key idea is to construct and estimate targeted subspaces that exclude the noise and irrelevant information in the data set. The research project is expected to make significant contributions on two fronts: computational and theoretical foundations for envelope subspace estimation in high dimensions, and efficient tensorial parameter estimation in regression and classification models.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.