Enhanced estimation method for partial scattering functions in contrast variation small-angle neutron scattering via Gaussian process regression with prior knowledge of smoothness

Contrast variation small-angle neutron scattering (CV-SANS) is a powerful tool for evaluating the structure of multi-component systems. In CV-SANS, the scattering intensities I(Q) measured with different scattering contrasts are de­com­posed into partial scattering functions S(Q) of the self- and cross-correlations between components. Since the measurement has a measurement error, S(Q) must be estimated statistically from I(Q). If no prior knowledge about S(Q) is available, the least-squares method is best, and this is the most popular estimation method. However, if prior knowledge is available, the estimation can be improved using Bayesian inference in a statistically authorized way. In this paper, we propose a novel method to improve the estimation of S(Q), based on Gaussian process regression using prior knowledge about the smoothness and flatness of S(Q). We demonstrate the method using synthetic core–shell and experimental polyrotaxane SANS data.