Our group develops algorithms for reconstructing particles from noisy diffraction patterns. Currently our efforts are directed at data taken with x-ray free electron lasers, such as the Linac Coherent Light Source. We also work closely with the group of Sol Gruner on image reconstruction in the limit of ultra low photon flux. Over the years we have noticed that our algorithms perform very well on some NP-hard problems; these applications have become a second line of research.