Joint Reconstruction of Image and Motion in MRI: Implicit Regularization Using an Adaptive 3D Mesh

Magnetic resonance images are affected by motion artefacts due to breathing and cardiac beating that occur during the acquisition. Methods for joint reconstruction of image and motion have been proposed recently. Such optimization problems are ill-conditioned, therefore regularization methods are required such as motion smoothness constraints using the Tikhonov method. However with Tikhonov methods the solution often relies on a good choice of the regularization parameter mu, especially in large parameter search spaces (e.g. in 3D reconstructions). In this paper, we propose an adaptive, implicit regularization method which results in subject-specific, spatially varying smoothness constraints on the motion model. It is based on the idea of solving for motion only in certain key points that form a mesh. A practical algorithm is proposed for generating this mesh automatically. The proposed method is shown to have a better convergence rate than the Tikhonov method, both in silico and in vivo. The accuracy of the reconstructed image and motion is also improved.