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Low Rank plus Sparse Decomposition of fMRI Data with Applications in Alzheimer’s Disease

  • Author / Creator
    Fu, Fangfang
  • Functional brain connectivity plays an important role on understanding
    how human brain functions and neuropsychological diseases such as Autism,
    Attention-deficit hyperactivity disorder (ADHD), and Alzheimer’s disease (AD).
    Functional Magnetic Resonance Imaging (fMRI) is one of the most powerful
    techniques to construct functional brain connectivity. However, the presence
    of potential outliers in fMRI BOLD signals might lead to unreliable results
    in construction. Another challenge of most existing connectivity construction
    methods is the results might not be stable. In this thesis, we propose a framework
    which is able to provide robust and stable connectivity. In particular,
    a low-rank plus sparse (L + S) matrix decomposition technique is adapted to
    decompose the resting state fMRI BOLD signals, where the low-rank matrix
    L recovers the essential common features from regions of interest (ROIs), and
    the sparse matrix S catches the sparse individual variability and potential outliers.
    Based on decomposition, various approaches can be applied to construct
    functional brain connectivity, such as correlation, partial correlation, Graphical
    Lasso and others. However, we propose to use the recently developed novel
    sparse matrix estimation based on concentration inequality. Statistical test for
    each connection is implemented for differentiating group difference. Through
    bootstrapping afterwards, we verify whether performing low-rank plus sparse
    matrix decomposition can achieve more stable and robust results.
    We apply our method on Alzheimer’s Disease Neuroimaging Initiative (ADNI)
    data, and compare the results with those based on original BOLD signals. We
    discover that the methods for building connectivities based on low rank matrices behave better than based on original BOLD signals, in the sense that
    the former can reveal and identify more significant ROI connections. We find
    that the recently proposed concentration inequality based method performs
    better overall compared with correlation, partial correlation, and Graphical
    Lasso method. We also obtain the first ten most significant connections for
    differentiating group differences for Alzheimer’s disease. Among them, the
    left hippocampus region and the left cerebellum 7 region is the most significant
    one, with p value smaller than 0.0005, which is consistent with existing
    literatures’ findings. Through bootstrapping, we verify that performing low rank
    plus sparse matrix decomposition can achieve more stable results for
    constructing functional brain connectivities.

  • Subjects / Keywords
  • Graduation date
    Fall 2018
  • Type of Item
    Thesis
  • Degree
    Master of Science
  • DOI
    https://doi.org/10.7939/R3ZG6GP7S
  • License
    Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.