  The super-resolution theory developed recently by Cand\`{e}s and
Fernandes-Granda aims to recover fine details of a sparse frequency spectrum
from coarse scale information only. The theory was then extended to the cases
with compressive samples and/or multiple measurement vectors. However, the
existing atomic norm (or total variation norm) techniques succeed only if the
frequencies are sufficiently separated, prohibiting commonly known high
resolution. In this paper, a reweighted atomic-norm minimization (RAM) approach
is proposed which iteratively carries out atomic norm minimization (ANM) with a
sound reweighting strategy that enhances sparsity and resolution. It is
demonstrated analytically and via numerical simulations that the proposed
method achieves high resolution with application to DOA estimation.
