Time-Dependent Deep Image Prior for Dynamic MRI

We propose a novel unsupervised deep-learning-based algorithm to solve the inverse problem found in dynamic magnetic resonance imaging (MRI). Our method needs neither prior training nor additional data; in particular, it does not require either electrocardiogram or spokes-reordering in the context of cardiac images. It generalizes to sequences of images the recently introduced deep-image-prior approach. The essence of the proposed algorithm is to proceed in two steps to fit k-space synthetic measurements to sparsely acquired dynamic MRI data. In the first step, we deploy a convolutional neural network (CNN) driven by a sequence of low-dimensional latent variables to generate a dynamic series of MRI images. In the second step, we submit the generated images to a nonuniform fast Fourier transform that represents the forward model of the MRI system. By manipulating the weights of the CNN, we fit our synthetic measurements to the acquired MRI data. The corresponding images from the CNN then provide the output of our system; their evolution through time is driven by controlling the sequence of latent variables whose interpolation gives access to the sub-frame---or even continuous---temporal control of reconstructed dynamic images. We perform experiments on simulated and real cardiac images of a fetus acquired through 5-spoke-based golden-angle measurements. Our results show improvement over the current state-of-the-art.