  High-quality training data are not always available in dynamic MRI. To
address this, we propose a self-supervised deep learning method called deep
image prior with structured sparsity (DISCUS) for reconstructing dynamic
images. DISCUS is inspired by deep image prior (DIP) and recovers a series of
images through joint optimization of network parameters and input code vectors.
However, DISCUS additionally encourages group sparsity on frame-specific code
vectors to discover the low-dimensional manifold that describes temporal
variations across frames. Compared to prior work on manifold learning, DISCUS
does not require specifying the manifold dimensionality. We validate DISCUS
using three numerical studies. In the first study, we simulate a dynamic
Shepp-Logan phantom with frames undergoing random rotations, translations, or
both, and demonstrate that DISCUS can discover the dimensionality of the
underlying manifold. In the second study, we use data from a realistic late
gadolinium enhancement (LGE) phantom to compare DISCUS with compressed sensing
(CS) and DIP, and to demonstrate the positive impact of group sparsity. In the
third study, we use retrospectively undersampled single-shot LGE data from five
patients to compare DISCUS with CS reconstructions. The results from these
studies demonstrate that DISCUS outperforms CS and DIP, and that enforcing
group sparsity on the code vectors helps discover true manifold dimensionality
and provides additional performance gain.
