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

In magnetic resonance imaging the spin-lattice relaxation time (T
₁
) of tissues is estimated from a set of T
₁
-weighted images. As the T
₁
estimation is a voxel-wise estimation, correct alignment of the T
₁
-weighted images is crucial for T
₁
mapping. Therefore, to correct for motion, the T
₁
-weighted images are often registered prior to the T
₁
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 T
₁
estimation. In this work, we propose a unified approach, where the motion estimation is integrated into the T
₁
estimation procedure. The motion model parameters and T
₁
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 T
₁
map compared to the conventional two-step approach.