Nonlinear motion separation via untrained generator networks with disentangled latent space variables and applications to cardiac MRI

In this paper, a nonlinear approach to separate different motion types in video data is proposed. This is particularly relevant in dynamic medical imaging (e.g. PET, MRI), where patient motion poses a significant challenge due to its effects on the image reconstruction as well as for its subsequent interpretation. Here, a new method is proposed where dynamic images are represented as the forward mapping of a sequence of latent variables via a generator neural network. The latent variables are structured so that temporal variations in the data are represented via dynamic latent variables, which are independent of static latent variables characterizing the general structure of the frames. In particular, different kinds of motion are also characterized independently of each other via latent space disentanglement using one-dimensional prior information on all but one of the motion types. This representation allows to freeze any selection of motion types, and to obtain accurate independent representations of other dynamics of interest. Moreover, the proposed algorithm is training-free, i.e., all the network parameters are learned directly from a single video. We illustrate the performance of this method on phantom and real-data MRI examples, where we successfully separate respiratory and cardiac motion.