Tensor Regressions and Applications in Neuroimaging Data Analysis

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Rapidly advancing medical imaging technologies are producing massive amounts of complex imaging data, and are imposing unprecedented demands for new statistical methodology. The investigators aim to integrate advanced statistical modeling with modern computational techniques to address some most challenging questions arising from medical imaging analysis. The investigators propose a novel statistical framework and develop accompanying theory and algorithms for tensor regression, i.e., regression with image covariates that are in the form of multidimensional arrays / tensors. They study a variety of regularization schemes in the context of tensor regression to stabilize estimation, improve risk property, and reconstruct sparse signals. They also develop methodology within the tensor regression framework for scientific applications including brain region and connectivity pattern identification, imaging based disease diagnosis, and multiple imaging modalities analysis. The project offers a systematic solution to a family of imaging data problems, and also provides a new class of statistical regression methods.One of the most intriguing questions in modern science is to understand human brains, both those of general population and those with neuropsychiatric and neurodegenerative disorders. Advanced medical imaging technologies provide powerful tools to help address the question, producing imaging data of unprecedented size and complexity. The investigators aim to develop a host of novel statistical methods, theories, and highly scalable algorithms for the analysis of massive medical imaging data. The proposed research is expected to make significant contributions on two fronts: timely response to the growing needs and challenges of neuroimaging data analysis, and development of an utterly new and broad statistical framework and the associated methodology that contributes to the advance of the statistical discipline.