In low energy electron point source (LEEPS) microscopy, electrons emerge from a point source, propagate as spherical waves, and arrive at a screen. Some electrons scatter off an object, i.e. a cluster of atoms, placed between the source and the screen; others arrive at the screen without scattering. The interference pattern on the screen, an electron hologram, is used to reconstruct the object by calculating and analyzing a function K(r) in the region occupied by the object. We present an iterative method that uses the original reconstruction K(o)(r) to determine the atomic configuration of the object. No knowledge of the object, except for the vicinity in which the object is located, is used in the iterative scheme. In particular, no knowledge of the atomic structure is used. The method uses K(o)(r) to make a test object that in turn gives another reconstruction K(1)(r); K(1)(r) and K(o)(r) are used to modify the test object and obtain K(2)(r). The iteration is repeated until it converges on a final object that gives a reconstruction K(f)(r) that is very similar to K(o)(r). The final object gives an atomic structure that is close to the atomic structure of the original object. Results for several idealized objects are presented and discussed.