  In this work, we develop several inference methods to estimate the position
of dislocations from images generated using dark-field X-ray microscopy (DFXM)
-- achieving superresolution accuracy and principled uncertainty
quantification. Using the framework of Bayesian inference, we incorporate
models of the DFXM contrast mechanism and detector measurement noise, along
with initial position estimates, into a statistical model coupling DFXM images
with the dislocation position of interest. We motivate several position
estimation and uncertainty quantification algorithms based on this model. We
then demonstrate the accuracy of our primary estimation algorithm on synthetic
realistic DFXM images of edge dislocations in single crystal aluminum. We
conclude with a discussion of our methods' impact on future dislocation studies
and possible future research avenues.
