Phase Retrieval Problem. Application to VLBI Mapping of Active Galactic   Nuclei
  The well-known phase problem which means image reconstruction from only spectrum magnitude without using any spectrum phase information is considered basically in application to VLBI mapping of compact extragalactic radio sources (active galactic nuclei). The method proposed for phaseless mapping is based on the reconstruction of the spectrum magnitude on the entire UV plane from the measured visibility magnitude on a limited set of points and the reconstruction of the sought-for image of the source by Fienup's error-reduction iterative algorithm from the spectrum magnitude reconstructed at the first stage. It is shown that the technique used ensures unique solution (within a class of equivalent functions) for AGNs with typical structure morphology "bright core + week jet". The method proposed can be used, for example, for imaging with ultra-high resolution using a space{ground radio interferometer with a space antenna in a very high orbit ("RadioAstron"). In this case, a multi-element interferometer essentially degenerates into a two-element interferometer and the degeneracy of the close-phase relations prevents the use of standard methods for hybrid mapping and self-calibration. The capabilities and restrictions of the method are demonstrated on a number of model experiments. For a few selected AGNs the images are obtained from VLBA observations. 
A. T. Bajkova
astro-ph.IM