Continuous q-Space Signal Synthesis from Arbitrary Sparse Multi-Shell Measurements

Diffusion MRI protocols with dense multi-shell and multi-direction sampling are time-consuming. We propose a protocol-agnostic model that reconstructs continuous q-space signals from sparse, variable acquisition sets without retraining. Given an arbitrary-size set of measurements (normalized signals with q-vectors √bg), a Perceiver-style set encoder infers SHORE coefficients, and an analytic SHORE decoder synthesizes signals at unseen b-values and directions. We inject local spatial context via a lightweight 3×3×3 neighborhood patch to improve robustness under extreme undersampling. Training masks, shells, and directions to mimic heterogeneous protocols, uses repulsion sampling with antipodal symmetry for diverse subsets, and applies physically consistent augmentation by querying the SHORE decoder at arbitrary b-values and directions, with weighted losses favoring real measurements. On held-out HCP subjects across multiple undersampling regimes, our method improves signal prediction and diffusion-derived metrics versus sparse SHORE fitting and neural baselines, enabling a single model for heterogeneous diffusion protocols. Our implementation is available on GitHub.