Coarse-to-Fine 3D MRI Reconstruction via 3D Neural Operators

3D MRI reconstruction with deep learning is limited not only by GPU memory and voxel data resolution but also by the tendency of standard neural networks to overfit to training discretizations (resolutions), which makes them highly sensitive to variations in image resolution and sampling patterns. This forces downsampling or dimensional collapse and restricts generalization to higher-resolution volumes. We present a new neural operator framework for learning local features backed by 3D discrete-continuous convolutions (DISCO), which are inherently resolution-agnostic. Unlike conventional 3D convolutions or kernel-interpolated weights, the proposed 3D neural operator relies on filters in a continuous domain, while preserving local inductive biases. This design enables training on coarse, low-memory volumes with full backpropagation, and supports high-resolution zero-shot or few-shot inference without aliasing, while reducing memory cost. This coarse-to-fine regime allows memory-efficient 3D training and large-volume testing using inference only. We evaluate the proposed 3D local neural operator on the SKM-TEA dataset for accelerated 3D MRI reconstruction, demonstrating accurate reconstructions with strong runtime and memory efficiency. While we focus on 3D MRI, the proposed 3D DISCO-based operator is broadly applicable to other 3D imaging modalities and general 3D voxel-based data reconstruction tasks.