Simultaneous motion correction and T1 estimation in quantitative T1 mapping: An ML restoration approach

In magnetic resonance imaging the spin-lattice relaxation time (T₁) of tissues is estimated from a set of T₁-weighted images. As the T₁ estimation is a voxel-wise estimation, correct alignment of the T₁-weighted images is crucial for T₁ mapping. Therefore, to correct for motion, the T₁-weighted images are often registered prior to the T₁ estimation. This two-step approach, however, does not provide an accurate motion detection due to the high dynamic contrast changes in the series of images. Moreover, interpolation effects during registration, propagate to the T₁ estimation. In this work, we propose a unified approach, where the motion estimation is integrated into the T₁ estimation procedure. The motion model parameters and T₁ parameters are jointly estimated using a Maximum Likelihood (ML) approach. Results on simulation and real data experiments show a substantial improvement in the precision and accuracy of the estimated T₁ map compared to the conventional two-step approach.