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

Deep-learning-based 3D MRI reconstruction is limited in practice by the GPU memory and compute cost of full-volume training. A common workaround is to train at lower resolution and run inference at higher resolution, but standard neural networks are resolution-specific and degrade substantially when evaluated outside the training setting. We instead use resolution-agnostic neural operators (NOs) and propose KIR-NO (k-space-to-Image Reconstruction Neural Operator), a coarse-to-fine, discretization-agnostic framework for accelerated 3D MRI reconstruction. KIR-NO is trained with full backpropagation on memory-feasible low-resolution volumes and applied zero-shot to higher-resolution volumes at inference, without fine-tuning. Its core building block is a 3D local neural operator based on discrete-continuous convolutions: convolutional filters are parameterized in a continuous basis (we propose and empirically compare two 3D bases, piecewise-linear and Morlet-wavelet) and sampled at arbitrary voxel resolutions while preserving the local inductive bias of convolution. KIR-NO integrates these learned operators with physics-based consistency: a k-space neural-operator head first refines the undersampled Fourier measurements, and image-space neural-operator cascades then refine the reconstruction through interleaved data-consistency updates. Across 3D knee (SKM-TEA) and brain (BraTS 2021) MRI benchmarks, KIR-NO consistently outperforms classical and CNN baselines: it improves over a state-of-the-art 3D CNN by 4.13 dB PSNR at half resolution under 4× acceleration on SKM-TEA, with gains persisting at 8× and 16×, and exceeds the same baseline by 13.63 dB under zero-shot full-resolution transfer on BraTS. Together, these results show that KIR-NO enables scalable, memory-efficient, and resolution-flexible 3D MRI reconstruction across anatomies.