Geometry-aware model-based deep learning for dynamic MR imaging

Abstract

Magnetic resonance imaging (MRI) is widely used for clinical diagnosis because it provides non-invasive, ionizing-radiation-free imaging with excellent soft-tissue contrast. However, the inherently prolonged acquisition makes it challenging to achieve high spatial resolution and high temporal resolution simultaneously, particularly in dynamic imaging applications such as cardiac cine MRI. Accelerated MRI addresses this limitation by acquiring undersampled k-space measurements and reconstructing images through regu larized inverse formulations. While conventional methods rely on handcrafted priors to regularize this ill-posed inverse problem, deep learning has substantially advanced accel erated MRI reconstruction by learning expressive data-driven priors from large datasets. In particular, model-based deep learning has emerged as a leading paradigm by unrolling iterative optimization algorithms and explicitly embedding the MRI forward model and data-consistency constraints into learnable architectures. Despite its strong performance, current model-based deep learning methods still have evident limitations and substantial room for improvement from the perspective of prior modeling. Specifically, a common yet essential class of structural information has not been systematically exploited, namely geometry-aware priors, including transformation symmetries, organ morphology cues, and motion-induced deformations, which collectively characterize the geometric properties of anatomical structures in both static anatomy and dynamic motion. Incorporating such priors in a principled manner can promote anatomically consistent reconstructions, im prove robustness and generalization across varying sampling patterns and imaging views, and reduce the risk of structurally implausible artifacts under severe undersampling. These considerations motivate an urgent need for systematic integration of geometry aware priors into model-based deep learning for accelerated dynamic MRI reconstruction.

To address this need, this thesis develops a systematic and theoretically grounded framework for geometry-aware model-based deep learning in accelerated dynamic MRI reconstruction. In particular, the framework leverages transformation symmetry priors through explicit rotation-equivariant convolutional design and accurate rotation-aware filter representation, while exploiting organ morphology cues and motion-induced defor mation priors via dynamics-adaptive deformable sampling to better follow anatomical boundaries and non-rigid motion. First, we propose Spatiotemporal Rotation-Equivariant Convolutions (SREC), a parameter-efficient convolutional layer architecture that explic itly enforces spatiotemporal rotational symmetry by structured weight sharing across orientations and frames. Building on SREC, we further introduce an end-to-end rotation equivariant deep unrolling framework, DUN-SRE, which adopts SREC as the core con volutional layers in both the proximal mapping and data-consistency components, en abling consistent propagation of symmetry priors throughout the reconstruction process. To address discretization and interpolation errors that undermine reliable rotation-aware modeling, we propose DF-Basis, a decoupled Fourier-basis filter parametrization that pa rameterizes the convolutional filters used in SREC (and thus DUN-SRE) and stabilizes arbitrary-angle rotations in the discrete setting with high representation accuracy. Fi nally, to better capture non-rigid motion and complex anatomical boundaries, we develop an efficient dynamics-adaptive spatiotemporal deformable convolution mechanism that provides adaptive sampling while controlling the computational overhead, complement ing the above symmetry-driven designs with deformation-adaptive modeling for dynamic MRI.

The proposed framework is evaluated on dynamic cardiac cine MRI across a range of acceleration factors and undersampling patterns. The results demonstrate that system atically integrating geometry-aware priors—leveraging transformation symmetry priors via rotation-equivariant unrolling (SREC/DUN-SRE) with high-accuracy rotation-aware filter parametrization (DF-Basis), and exploiting organ morphology and motion-induced deformation priors via dynamics-adaptive deformable sampling—consistently improves reconstruction fidelity, yielding fewer undersampling artifacts, sharper delineation of fine anatomical boundaries, and stronger spatiotemporal coherence across frames. Moreover, the geometry-aware designs exhibit improved robustness and generalization under differ ent sampling strategies, imaging views, and challenging motion conditions, particularly in high-acceleration regimes where geometric consistency is critical for anatomical plausi bility, thereby supporting high-fidelity dynamic MRI reconstruction under severe k-space undersampling.

Date of Award	18 Jul 2026
Original language	English
Awarding Institution	University of Nottingham
Supervisor	Chengbo Wang (Supervisor), Jianfeng Ren (Supervisor), Dong Liang (Supervisor) & Paul Glover (Supervisor)