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

  • fMRI
  • Alzheimer’s Disease
  • Low rank plus sparse matrix decomposition

• Graduation date

  Fall 2018

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/R3ZG6GP7S

• License

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