title: Maximum likelihood estimation for second level fMRI data analysis with expectation trust region algorithm.
abstract: The trust region method which originated from the Levenberg-Marquardt (LM) algorithm for mixed effect model estimation are considered in the context of second level functional magnetic resonance imaging (fMRI) data analysis. We first present the mathematical and optimization details of the method for the mixed effect model analysis, then we compare the proposed methods with the conventional expectation-maximization (EM) algorithm based on a series of datasets (synthetic and real human fMRI datasets). From simulation studies, we found a higher damping factor for the LM algorithm is better than lower damping factor for the fMRI data analysis. More importantly, in most cases, the expectation trust region algorithm is superior to the EM algorithm in terms of accuracy if the random effect variance is large. We also compare these algorithms on real human datasets which comprise repeated measures of fMRI in phased-encoded and random block experiment designs. We observed that the proposed method is faster in computation and robust to Gaussian noise for the fMRI analysis. The advantages and limitations of the suggested methods are discussed.
authors: Intelligent Systems Research Centre, University of Ulster, Magee Campus, Derry, BT487JL Northern Ireland, UK. Electronic address: xingfengli@gmail.com.
authors: Xingfeng
authors: X
authors: Li
authors: Intelligent Systems Research Centre, University of Ulster, Magee Campus, Derry, BT487JL Northern Ireland, UK.
authors: Damien
authors: D
authors: Coyle
authors: Intelligent Systems Research Centre, University of Ulster, Magee Campus, Derry, BT487JL Northern Ireland, UK.
authors: Liam
authors: L
authors: Maguire
authors: Intelligent Systems Research Centre, University of Ulster, Magee Campus, Derry, BT487JL Northern Ireland, UK.
authors: Thomas Martin
authors: TM
authors: McGinnity
mesh_terms: D000465:Algorithms; D001921:Brain / Q000502:physiology*; D001931:Brain Mapping / Q000379:methods; D003198:Computer Simulation; D006439:Hemodynamics; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods; D016013:Likelihood Functions; D008279:Magnetic Resonance Imaging / Q000379:methods*; D016011:Normal Distribution; D011336:Probability; D012044:Regression Analysis
keywords: Maximum Log Likelihood (LL) estimation; Mixed effect model; Second level fMRI data analysis; Trust region algorithm; Variance analysis