A deconvolution method for diffraction measurements based on a statistical learning technique is presented. The radial-basis function network is used to model the underlying function. A full probabilistic description of the measurement is introduced, incorporating a Bayesian algorithm based on an evidence framework. This method allows predictions of both the convolution and the underlying function from noisy measurements. In addition, the method can provide an estimation of the prediction uncertainty, i.e. error-bars. In order to assess the capability of the method, the model was tested first on synthetic data of controllable quality and sparsity; it is shown that the method works very well, even for inaccurately measured (noisy) data. Subsequently, the deconvolution method was applied to real data sets typical of neutron and synchrotron residual stress (strain) data, recovering features not immediately evident in the large-gauge-volume measurements themselves. Finally, the extent to which short-period components are lost as a function of the measurement gauge dimensions is discussed. The results seem to indicate that for a triangular sensor-sensitivity function, measurements are best made with a gauge of a width approximately equal to the wavelength of the expected strain variation, but with a significant level of overlap (∼80%) between successive points; this is contrary to current practice for neutron strain measurements.
Xiong, Y.-S., & Withers, P. J. (2006). A deconvolution method for the reconstruction of underlying profiles measured using large sampling volumes. Journal of Applied Crystallography, 39(3), 410–424. https://doi.org/10.1107/s0021889806012210