The problem of reconstructing three-dimensional objects from a set of two-dimensional projected images has arisen and been solved independently in fields ranging from medicine and electron microscopy to holographic interferometry. By using a source of radiation external to the object, we obtain a transmission picture or projection of the three-dimensional object onto a two-dimensional surface such as the film of an ordinary electron micrograph or x-ray. The reconstruction problem is: Given a subset of all possible projections of an object, estimate its internal density distribution.