  In this work, super-resolution by 4 compressive sensing methods (OMP, BP,
BLOOMP, BP-BLOT) with highly coherent partial Fourier measurements is
comparatively studied. An alternative metric more suitable for gauging the
quality of spike recovery is introduced and based on the concept of filtration
with a parameter representing the level of tolerance for support offset. In
terms of the filtered error norm only BLOOMP and BP-BLOT can perform
grid-independent recovery of well separated spikes of Rayleigh index 1 for
arbitrarily large super-resolution factor. Moreover both BLOOMP and BP-BLOT can
localize spike support within a few percent of the Rayleigh length. This is a
weak form of super-resolution. Only BP-BLOT can achieve this feat for closely
spaced spikes separated by a fraction of the Rayleigh length, a strong form of
super-resolution.
