In this work we present a framework for reliably detecting significant differences in quantitative magnetic resonance imaging and evaluate it with diffusion tensor imaging (DTI) experiments. As part of this framework we propose a new spatially regularized maximum likelihood estimator that simultaneously estimates the quantitative parameters and the spatially-smoothly-varying noise level from the acquisitions. The noise level estimation method does not require repeated acquisitions. We show that the amount of regularization in this method can be set a priori to achieve a desired coefficient of variation of the estimated noise level. The noise level estimate allows the construction of a Cramér-Rao-lower-bound based test statistic that reliably assesses the significance of differences between voxels within a scan or across different scans. We show that the regularized noise level estimate improves upon existing methods and results in a substantially increased precision of the uncertainty estimates of the DTI parameters. It enables correct specification of the null distribution of the test statistic and with it the test statistic obtains the highest sensitivity and specificity. The source code of the estimation framework, test statistic and experiment scripts are made available to the community.

Cramér-Rao lower bound, diffusion tensor imaging (DTI), quantitative magnetic resonance imaging (qMRI), regularization, statistical noise analysis, statistical testing,
IEEE Transactions on Medical Imaging
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Poot, D.H.J, & Klein, S. (2015). Detecting statistically significant differences in quantitative MRI experiments, applied to diffusion tensor imaging. IEEE Transactions on Medical Imaging, 34(5), 1164–1176. doi:10.1109/TMI.2014.2380830