A major challenge of the long measurement times in magnetic resonance imaging (MRI), an important medical imaging technology, is that patients may move during data acquisition. This leads to severe motion artifacts in the reconstructed images and volumes. In this paper, we propose MotionTTT a deep learning-based test-time-training (TTT) method for accurate motion estimation. The key idea is that a neural network trained for motion-free reconstruction has a small loss if there is no motion, thus optimizing over motion parameters passed through the reconstruction network enables accurate estimation of motion. The estimated motion parameters enable to correct for the motion and to reconstruct accurate motion-corrected images. Our method uses 2D reconstruction networks to estimate rigid motion in 3D, and constitutes the first deep learning based method for 3D rigid motion estimation towards 3D-motion-corrected MRI. We show that our method can provably reconstruct motion parameters for a simple signal and neural network model. We demonstrate the effectiveness of our method for both retrospectively simulated motion and prospectively collected real motion-corrupted data. Code is available at \url{https://github.com/MLI-lab/MRI_MotionTTT}.

Water-fat separation is a non-linear non-convex parameter estimation problem in magnetic resonance imaging typically solved using spatial constraints. However, there is still limited knowledge on how to separate in vivo three chemical species in the presence of magnetic field inhomogeneities. The proposed method uses multiple graph-cuts in a hierarchical multi-resolution framework to perform robust chemical species separation in the breast for subjects with and without silicone implants. Experimental results show that the proposed method can decrease the computational time for water-fat separation and perform accurate water-fat-silicone separation with only a limited number of acquired echo images at 3 T. The silicone-separated images have an improved spatial resolution and image contrast compared to conventional scans used for regular monitoring of the silicone implant's integrity.