NSF-Research Training Group
Project: Removing noise from tensor-valued neuroimaging data
Mentors: Owen Carmichael (Neuroscience), Debashis Paul (Statistics) and Jie Peng (Statistics)
Diffusion magnetic resonance imaging (MRI) provides, at hundreds of thousands of locations in the human brain, measurements of the spatial distribution of local water diffusion, which are then used to infer the pathways of neuron connections throughout the brain. The raw MRI measurements are used to estimate a 3x3 positive definite matrix (i.e., a tensor) at each location, but the measurements are notoriously noisy, so removing noise from the data during tensor estimation is essential. In this project, the student will learn the fundamentals of the tensor estimation problem, and linear regression approaches for removing noise from the data during tensor estimation. The student will implement various schemes for tensor estimation and apply them to synthetic data and real diffusion MRI scans of young people, healthy elderly people, and elderly people with brain diseases including Alzheimer's disease. Pre-requisites include STA 108 and STA 141, with a strong working knowledge of regression and ability to program in R or Matlab.