Benchmark problems for phase retrieval

The hardest instances of phase retrieval arise in crystallography, where the signal is periodic and comprised of atomic distributions arranged uniformly in the unit cell of the crystal. We have constructed a graded set of benchmark problems for evaluating algorithms that perform this type of phase retrieval. A simple iterative algorithm was used to establish baseline runtimes that empirically grow exponentially in the sparsity of the signal autocorrelation. We also review the algorithms used by the leading software packages for crystallographic phase retrieval.