  This paper deals with modelling and reconstruction of strain fields, relying
upon data generated from neutron Bragg-edge measurements. We propose a
probabilistic approach in which the strain field is modelled as a Gaussian
process, assigned a covariance structure customised by incorporation of the
so-called equilibrium constraints. The computational complexity is
significantly reduced by utilising an approximation scheme well suited for the
problem. We illustrate the method on simulations and real data. The results
indicate a high potential and can hopefully inspire the concept of
probabilistic modelling to be used within other tomographic applications as
well.

Data Analysis, Statistics and Probability