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>I</i>(<i>Q</i>) measured with different scattering contrasts are de-com-posed into partial scattering functions <i>S</i>(<i>Q</i>) of the self- and cross-correlations between components. Since the measurement has a measurement error, <i>S</i>(<i>Q</i>) must be estimated statistically from <i>I</i>(<i>Q</i>). If no prior knowledge about <i>S</i>(<i>Q</i>) 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 <i>S</i>(<i>Q</i>), based on Gaussian process regression using prior knowledge about the smoothness and flatness of <i>S</i>(<i>Q</i>). We demonstrate the method using synthetic core-shell and experimental polyrotaxane SANS data.