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 “true” scene via qMRI, due to measurement errors or unpredictable influences. We use a hidden Markov Random Field to model the unobserved “true” scene 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. Moreover, we focus on recovering the “true” scene rather than segmenting the image. 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.
Zhang, Xiaoxi ; Johnson, Timothy D.; and Little, Roderick J.A., "Quantitative Magnetic Resonance Image Analysis via the EM Algorithm with Stochastic Variation" (May 2007). The University of Michigan Department of Biostatistics Working Paper Series. Working Paper 72.