  The baryon acoustic oscillations are a promising route to the precision
measure of the cosmological distance scale and hence the measurement of the
time evolution of dark energy. We show that the non-linear degradation of the
acoustic signature in the correlations of low-redshift galaxies is a
correctable process. By suitable reconstruction of the linear density field,
one can sharpen the acoustic peak in the correlation function or, equivalently,
restore the higher harmonics of the oscillations in the power spectrum. With
this, one can achieve better measurements of the acoustic scale for a given
survey volume. Reconstruction is particularly effective at low redshift, where
the non-linearities are worse but where the dark energy density is highest. At
z=0.3, we find that one can reduce the sample variance error bar on the
acoustic scale by at least a factor of 2 and in principle by nearly a factor of
4. We discuss the significant implications our results have for the design of
galaxy surveys aimed at measuring the distance scale through the acoustic peak.
