Tomography with unknown view angles

We address the problem of parallel beam tomographic reconstruction when the angles at which the projections are taken are unknown. The problem arises in medical imaging owing to patient motion, and in imaging of viruses from a single projection of many identical units at random orientations. We determine conditions for unique identifiability of the angles from the projection data alone, and derive bounds on the variance of estimators of those angles in the presence of noise. Finally, we present a maximum likelihood estimator, along with a heuristic initialization procedure. Numerical simulations on a test phantom show excellent agreement with the bounds, and nearly perfect reconstructions at moderate noise levels.