  We consider the problem of mapping with ultra-high angular resolution using a
space-ground radio interferometer with a space antenna in a high orbit,whose
apogee height exceeds the radius of the Earth by a factor of ten. In this case,
a multielement interferometer essentially degenerates into a two-element
interferometer. The degeneracy of the close-phase relations prevents the use of
standard methods for hybrid mapping and self-calibration for the correct
reconstruction of images. We propose a new phaseless mapping method based on
methods for the reconstruction of images in the complete absence of phase
information, using only the amplitudes of the spatial-coherence function of the
source. In connection with this problem, we propose a new method for the
reliable solution of the phase problem, based on optimizing
information-carrying nonlinear functionals, in particular, the Shannon entropy.
Results of simulations of mapping radio sources with various structures with
ultra-high angular resolution in the framework of the RADIOASTRON mission are
presented.
