Bias correction of maximum likelihood estimation in quantitative MRI

For quantitative MRI techniques, such as T1, T2 mapping and Diffusion Tensor Imaging (DTI), a model has to be fit to several MR images that are acquired with suitably chosen different acquisition settings. The most efficient estimator to retrieve the parameters is the Maximum Likelihood (ML) estimator. However, the standard ML estimator is biased for finite sample sizes. In this paper we derive a bias correction formula for magnitude MR images. This correction is applied in two different simulation experiments, a T2 mapping experiment and a DTI experiment. We show that the correction formula successfully removes the bias. As the correction is performed as post-processing, it is possible to retrospectively correct the results of previous quantitative experiments. With this procedure more accurate quantitative values can be obtained from quantitative MR acquisitions.