We consider beams that are described by a four-dimensional (4D) transverse distribution f (x, y, x′, y′), where x′ ≡ px /pz and z is the axial coordinate. A two-slit scanner is commonly employed to measure, over a sequence of shots, a two-dimensional (2D) projection of such a beam's phase space, for example, f (x, x′). Another scanner might yield f (y, y′) or, using crossed slits, f (x, y). A small set of such 2D scans does not uniquely specify f (x, y, x′, y′). We have developed “tomographic” techniques to synthesize a “reasonable” set of particles in a 4D phase space having 2D densities consistent with the experimental data. We briefly summarize one method and describe progress in validating it, using simulations of the High Current Experiment at Lawrence Berkeley National Laboratory.