A Unified Maximum Likelihood Framework for Simultaneous Motion and $T_{1}$ Estimation in Quantitative MR $T_{1}$ Mapping.

Abstract

In quantitative MR T₁ mapping, the spin-lattice relaxation time T₁ of tissues is estimated from a series of T₁ -weighted images. As the T₁ estimation is a voxel-wise estimation procedure, correct spatial alignment of the T₁ -weighted images is crucial. Conventionally, the T₁ -weighted images are first registered based on a general-purpose registration metric, after which the T₁ map is estimated. However, as demonstrated in this paper, such a two-step approach leads to a bias in the final T₁ map. In our work, instead of considering motion correction as a preprocessing step, we recover the motion-free T₁ map using a unified estimation approach. In particular, we propose a unified framework where the motion parameters and the T₁ map are simultaneously estimated with a Maximum Likelihood (ML) estimator. With our framework, the relaxation model, the motion model as well as the data statistics are jointly incorporated to provide substantially more accurate motion and T₁ parameter estimates. Experiments with realistic Monte Carlo simulations show that the proposed unified ML framework outperforms the conventional two-step approach as well as state-of-the-art model-based approaches, in terms of both motion and T₁ map accuracy and mean-square error. Furthermore, the proposed method was additionally validated in a controlled experiment with real T₁ -weighted data and with two in vivo human brain T₁ -weighted data sets, showing its applicability in real-life scenarios.