We present a robust algorithm that uses a few snapshots of uniform line array (ULA) data to super-resolve multiple main-beam signals even in the presence of mainlobe interferers. This is done by splitting the ULA into two sets of sub-apertures and beamforming each by applying vectors of fixed and adaptive weights, with the adaptive weights constrained so as to preserve the signal-containing spatial-response region of interest. The thus-processed data-snapshots are then used to optimally estimate the mapping inter-relating both sets of sub-apertures. The eigenvalues of such mapping contain the super-resolved spatial locations of the main-beam signals of interest.