Maximum entropy - a new approach to the crystallographic phase problem

We have recently drawn the attention of crystallographers to the maximum entropy method (MEM) of image reconstruction which has found application in radio astronomy and geophysics. In this article, we review the theory of the MEM as applied to the crystallographic phase problem and discuss points of similarity, and differences, with conventional techniques. We then present a number of illustrative calculations in two and three dimensions on simulated and real structures. These examples show that the MEM can be used for phase refinement from partially known phases. say in macromolecular crystallography, and also for solving crystal structures ab initio using only measured Fourier amplitudes. With improved algorithms the method promises to become competitive with current techniques in crystal structure analysis