The Annals of Applied Statistics

Quantitative magnetic resonance image analysis via the EM algorithm with stochastic variation

Xiaoxi Zhang, Timothy D. Johnson, Roderick J. A. Little, and Yue Cao

Full-text: Open access

Abstract

Quantitative Magnetic Resonance Imaging (qMRI) provides researchers insight into pathological and physiological alterations of living tissue, with the help of which researchers hope to predict (local) therapeutic efficacy early and determine optimal treatment schedule. However, the analysis of qMRI has been limited to ad-hoc heuristic methods. Our research provides a powerful statistical framework for image analysis and sheds light on future localized adaptive treatment regimes tailored to the individual’s response. We assume in an imperfect world we only observe a blurred and noisy version of the underlying pathological/physiological changes via qMRI, due to measurement errors or unpredictable influences. We use a hidden Markov random field to model the spatial dependence in the data and develop a maximum likelihood approach via the Expectation–Maximization algorithm with stochastic variation. An important improvement over previous work is the assessment of variability in parameter estimation, which is the valid basis for statistical inference. More importantly, we focus on the expected changes rather than image segmentation. Our research has shown that the approach is powerful in both simulation studies and on a real dataset, while quite robust in the presence of some model assumption violations.

Article information

Source
Ann. Appl. Stat., Volume 2, Number 2 (2008), 736-755.

Dates
First available in Project Euclid: 3 July 2008

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1215118536

Digital Object Identifier
doi:10.1214/07-AOAS157

Mathematical Reviews number (MathSciNet)
MR2524354

Zentralblatt MATH identifier
05591296

Keywords
EM algorithm hidden Markov random field missing data model selection quantitative MRI stochastic variation

Citation

Zhang, Xiaoxi; Johnson, Timothy D.; Little, Roderick J. A.; Cao, Yue. Quantitative magnetic resonance image analysis via the EM algorithm with stochastic variation. Ann. Appl. Stat. 2 (2008), no. 2, 736--755. doi:10.1214/07-AOAS157. https://projecteuclid.org/euclid.aoas/1215118536


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