  This work applies Bayesian experimental design to selecting optimal
projection geometries in (discretized) parallel beam X-ray tomography assuming
the prior and the additive noise are Gaussian. The introduced greedy exhaustive
optimization algorithm proceeds sequentially, with the posterior distribution
corresponding to the previous projections serving as the prior for determining
the design parameters, i.e. the imaging angle and the lateral position of the
source-receiver pair, for the next one. The algorithm allows redefining the
region of interest after each projection as well as adapting parameters in the
(original) prior to the measured data. Both A and D-optimality are considered,
with emphasis on efficient evaluation of the corresponding objective functions.
Two-dimensional numerical experiments demonstrate the functionality of the
approach.
