  The reconstruction of the initial conditions of the Universe is an important
topic in cosmology, particularly in the context of sharpening the measurement
of the baryon acoustic oscillation (BAO) peak. Nonlinear reconstruction
algorithms developed in recent years, when applied to late-time matter fields,
can recover to a substantial degree the initial density distribution, however,
when applied to sparse tracers of the matter field, the performance is poorer.
In this paper we apply the Shi et al. non-linear reconstruction method to
biased tracers in order to establish what factors affect the reconstruction
performance. We find that grid resolution, tracer number density and mass
assignment scheme all have a significant impact on the performance of our
reconstruction method, with triangular-shaped-cloud (TSC) mass assignment and a
grid resolution of ${\sim}1{-}2h^{-1}$ Mpc being the optimal choice. We also
show that our method can be easily adapted to include generic tracer biases up
to quadratic order in the reconstruction formalism. Applying the reconstruction
to halo and galaxy samples with a range of tracer number densities, we find
that the linear bias is by far the most important bias term, while including
nonlocal and nonlinear biases only leads to marginal improvements on the
reconstruction performance. Overall, including bias in the reconstruction
substantially improves the recovery of BAO wiggles, down to
$k\sim0.25~h\text{Mpc}^{-1}$ for tracer number densities between
$2\times10^{-4}$ and $2\times10^{-3}~(h^{-1}\text{Mpc})^{-3}$.
