E2D-Unroll: efficient equivariant deformable unrolling networks for cardiac cine MRI reconstruction

Objective. Deep unrolling methods have achieved notable success in cardiac cine MRI reconstruction. However, their effectiveness is often constrained by the limited receptive field of shallow subnetworks and the rigid sampling of standard convolutions on fixed grids. Existing solutions such as transformer-based or multi-scale architectures can enlarge the receptive field, but typically introduce substantial increases in computational cost and model size. This work aims to enlarge the receptive field and improve spatiotemporal feature modeling while keeping the reconstruction model computationally lightweight and parameter-efficient. Approach. We propose an efficient equivariant deformable unrolling network (E2D-Unroll) that integrates three key components: a spatiotemporal deformable module (STDM), a rotation equivariant module (REM), and a gated orientation module (GOM). Specifically, STDM expands the receptive field and adaptively adjusts sampling locations to better capture spatiotemporal features. Next, REM embeds deformable convolutions into a rotation-equivariant framework, allowing kernels to be shared across orientations and thereby improving parameter efficiency. Building upon REM, GOM selectively emphasizes informative orientations to improve the utilization of rotation-equivariant representations. Main results. Extensive experiments on an in-house cardiac cine MRI dataset and the public OCMR dataset demonstrate that E2D-Unroll consistently outperforms state-of-the-art methods in reconstruction accuracy. Significance. E2D-Unroll unifies spatiotemporal deformable convolutions with rotation-equivariant networks to suppress large-scale aliasing artifacts more effectively while maintaining high parameter efficiency and low computational cost, providing a practical solution for accelerated cardiac cine MRI in real-world settings.