Cross-sectional MRI Data Analysis Based on Shearlet Transformation

Abstract

In this thesis, I will explore the various efficient shearlet representations of the Magnetic Resonance Imaging (MRI) data and how they can be further used in classical statistical analysis to shed a light on the early diagnosis of the Alzheimer’s disease (AD). The cause of AD is not completely understood yet. Studies results show the disease is associated with plaques and tangles. MRI, which provides an image of the structure of the brain without invasive data acquisition, has been actively studied to understand the progression of the disease in the recent decade. The complexity and dimensionality of MRI data poses challenges in utilizing them, and only simple summary statistics are extracted from MRI and used in many analyses. In my thesis, instead of extracting summary statistics from MRI based on subjective choice or knowledge, I propose to apply the state-of-art shearlet transformation to the original MRI data. Different from a standard wavelet representation, a shearlet representation is redundant but efficient by allowing additional angle (shear) parameters. This is especially powerful in detecting the edges in the images. Most informative shearlet coefficients are objectively selected based on the variation and the correlation with response variables. Principal Components Analysis (PCA) is further applied for deeper data reduction. Finally, a few leading linear combinations of the shearlet coefficients from the MRI data are included in a logistic regression to facilitate the diagnosis of AD. The power of the model is checked in a testing dataset and compared with the model without MRI data using receiver operating characteristic curves.

Committee Chair

Jimin Ding

Comments

Permanent URL: https://doi.org/10.7936/K798850W

Degree

Master of Arts (AM/MA)

Author's Department

Statistics

Author's School

Graduate School of Arts and Sciences

Document Type

Thesis

Date of Award

Spring 5-15-2014

Language

English (en)

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