Multiple Testing for Neuroimaging via Hidden Markov Random Field

Traditional voxel-level multiple testing procedures in neuroimaging, mostly $p$-value based, often ignore the spatial correlations among neighboring voxels and thus suffer from substantial loss of power. We extend the local-significance-index based procedure originally developed for the hidden Markov chain models, which aims to minimize the false nondiscovery rate subject to a constraint on the false discovery rate, to three-dimensional neuroimaging data using a hidden Markov random field model. A generalized expectation-maximization algorithm for maximizing the penalized likelihood is proposed for estimating the model parameters. Extensive simulations show that the proposed approach is more powerful than conventional false discovery rate procedures. We apply the method to the comparison between mild cognitive impairment, a disease status with increased risk of developing Alzheimer's or another dementia, and normal controls in the FDG-PET imaging study of the Alzheimer's Disease Neuroimaging Initiative.Comment: A MATLAB package implementing the proposed FDR procedure is available with this paper at the Biometrics website on Wiley Online Librar

High Dimensional Dependent Data Analysis for Neuroimaging.

This dissertation contains three projects focusing on two major high-dimensional problems for dependent data, particularly neuroimaging data: multiple testing and estimation of large covariance/precision matrices. Project 1 focuses on the multiple testing problem. Traditional voxel-level false discovery rate (FDR) controlling procedures for neuroimaging data often ignore the spatial correlations among neighboring voxels, thus suffer from substantial loss of efficiency in reducing the false non-discovery rate. We extend the one-dimensional hidden Markov chain based local-significance-index procedure to three-dimensional hidden Markov random field (HMRF). To estimate model parameters, a generalized EM algorithm is proposed for maximizing the penalized likelihood. Simulations show increased efficiency of the proposed approach over commonly used FDR controlling procedures. We apply the method to the comparison between patients with mild cognitive impairment and normal controls in the ADNI FDG-PET imaging study. Project 2 considers estimating large covariance and precision matrices from temporally dependent observations, in particular, the resting-state functional MRI (rfMRI) data in brain functional connectivity studies. Existing work on large covariance and precision matrices is primarily for i.i.d. observations. The rfMRI data from the Human Connectome Project, however, are shown to have long-range memory. Assuming a polynomial-decay-dominated temporal dependence, we obtain convergence rates for the generalized thresholding estimation of covariance and correlation matrices, and for the constrained $ell_1$ minimization and the $ell_1$ penalized likelihood estimation of precision matrix. Properties of sparsistency and sign-consistency are also established. We apply the considered methods to estimating the functional connectivity from single-subject rfMRI data. Project 3 extends Project 2 to multiple independent samples of temporally dependent observations. This is motivated by the group-level functional connectivity analysis using rfMRI data, where each subject has a sample of temporally dependent image observations. We use different concentration inequalities to obtain faster convergence rates than those in Project 2 of the considered estimators for multi-sample data. The new proof allows more general within-sample temporal dependence. We also discuss a potential way of improving the convergence rates by using a weighted sample covariance matrix. We apply the considered methods to the functional connectivity estimation for the ADHD-200 rfMRI data.PhDBiostatisticsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133198/1/haishu_1.pd

Deterministic Constructions of Binary Measurement Matrices from Finite Geometry

Deterministic constructions of measurement matrices in compressed sensing (CS) are considered in this paper. The constructions are inspired by the recent discovery of Dimakis, Smarandache and Vontobel which says that parity-check matrices of good low-density parity-check (LDPC) codes can be used as {provably} good measurement matrices for compressed sensing under $\ell_1$-minimization. The performance of the proposed binary measurement matrices is mainly theoretically analyzed with the help of the analyzing methods and results from (finite geometry) LDPC codes. Particularly, several lower bounds of the spark (i.e., the smallest number of columns that are linearly dependent, which totally characterizes the recovery performance of $\ell_0$-minimization) of general binary matrices and finite geometry matrices are obtained and they improve the previously known results in most cases. Simulation results show that the proposed matrices perform comparably to, sometimes even better than, the corresponding Gaussian random matrices. Moreover, the proposed matrices are sparse, binary, and most of them have cyclic or quasi-cyclic structure, which will make the hardware realization convenient and easy.Comment: 12 pages, 11 figure