Imaging techniques in radio interferometry often face a significant challenge posed by the large number of antenna signals received, from which the image information needs to be extracted. Beamforming is envisaged to reduce the rate required for transporting data from groups of antennas to a central site for further processing. We propose a novel method for image reconstruction based on the iterative scanning of a region of interest, combined with randomized beamforming. A modified approximate message-passing algorithm
is adopted to extract relevant image information from beamformed signals received at the antenna stations. The method is illustrated by simulations, with reference to the LOFAR radio interferometer, and compared with the CLEAN algorithm.