  Time-of-flight neutron imaging offers complementary attenuation contrast to
X-ray computed tomography (CT), coupled with the ability to extract additional
information from the variation in attenuation as a function of neutron energy
(time of flight) at every point (voxel) in the image. In particular Bragg edge
positions provide crystallographic information and therefore enable the
identification of crystalline phases directly. Here we demonstrate Bragg edge
tomography with high spatial and spectral resolution. We propose a new
iterative tomographic reconstruction method with a tailored regularisation term
to achieve high quality reconstruction from low-count data, where conventional
filtered back-projection (FBP) fails. The regularisation acts in a separated
mode for spatial and spectral dimensions and favours characteristic piece-wise
constant and piece-wise smooth behaviour in the respective dimensions. The
proposed method is compared against FBP and a state-of-the-art regulariser for
multi-channel tomography on a multi-material phantom. The proposed new
regulariser which accommodates specific image properties outperforms both
conventional and state-of-the-art methods and therefore facilitates Bragg edge
fitting at the voxel level. The proposed method requires significantly shorter
exposure to retrieve features of interest. This in turn facilitates more
efficient usage of expensive neutron beamline time and enables the full
utilisation of state-of-the-art high resolution detectors.
