Bayesian inference of anisotropic 2D small-angle scattering from sparse measurement

We present a Bayesian inference framework for reconstructing anisotropic two-dimensional small-angle scattering (2D SAS) patterns from sparse, noisy, or partially missing data. The method combines a symmetry-aware angular basis with radial Gaussian process priors to enable accurate, training-free interpolation and denoising. Computational benchmarks demonstrate reliable recovery of both isotropic and high-order anisotropic features under severe data reduction. Experimental validations on stretched polymers, sheared wormlike micelles, and carbon fibers show improved fidelity and resolution compared to raw measurements, achieving comparable accuracy with up to 50-fold fewer detected neutrons. This approach enables quantitative structural analysis under low-flux, time-limited, or single-shot conditions, extending the applicability of 2D SAS techniques to compact neutron sources and mechanically driven soft matter systems undergoing transient structural changes.