Non-iterative relative bias correction for 3D reconstruction of in utero fetal brain MR imaging

The slice intersection motion correction (SIMC) method is a powerful tool to compensate for motion that occurs during in utero acquisition of the multislice magnetic resonance (MR) images of the human fetal brain. The SIMC method makes use of the slice intersection intensity profiles of orthogonally planned slice pairs to simultaneously correct for the relative motion occurring between all the acquired slices. This approach is based on the assumption that the bias field is consistent between slices. However, for some clinical studies where there is a strong bias field combined with significant fetal motion relative to the coils, this assumption is broken and the resulting motion estimate and the reconstruction to a 3D volume can both contain errors. In this work, we propose a method to correct for the relative differences in bias field between all slice pairs. For this, we define the energy function as the mean square difference of the intersection profiles, that is then minimized with respect to the bias field parameters of the slices. A non iterative method which considers the relative bias between each slice simultaneously is used to efficiently remove inconsistencies. The method, when tested on synthetic simulations and actual clinical imaging studies where bias was an issue, brought a significant improvement to the final reconstructed image.