ABSTRACT
Until recently, these theoretical advances were not accompanied by corresponding experimental advances, and, like economics, image processing had acquired the reputation of something of a dismal science. For the X-ray community, a major breakthrough therefore occurred in 1998, with the first inversion of an experimental diffraction pattern to an image of a non-periodic object [17] at about 100nm resolution. Since then we have seen experimental three-dimensional reconstructions at higher resolution [3]. Since the early Gerchberg-Saxton papers, little experimental research was
undertaken using electron beams based on the HIO algorithm until the recent reconstructions of small holes [18] and the atomic-resolution image of a nanotube mentioned earlier [2]. Looking back, we see how crucial results in one field were ignored by others for decades, how important are interdisciplinary review articles, and how powerful is the recent synergy in this field between astronomers, X-ray crystallographers, the signal processing community, applied mathematics and electron microscopy.
