  Recent development in the reconstruction of the large-scale structure (LSS)
has seen significant improvement in restoring the linear baryonic acoustic
oscillation (BAO) from at least the non-linear matter field. This outstanding
performance is achieved by iteratively solving the Monge-Ampere equation of the
mass conservation. However, this technique also relies on several assumptions
that are not valid in reality, namely the longitudinal displacement, the
absence of shell-crossing and homogeneous initial condition. In particular, the
conservation equation of the tracers comprises the biasing information that
breaks down the last assumption. Consequently, direct reconstruction would
entangle the non-linear displacement with complicated bias parameters and
further affect the BAO. In this paper, we formulate a theoretical model
describing the reconstructed biased map by matching the tracer overdensity with
an auxiliary fluid with vanishing initial perturbation. Regarding the
performance of the reconstruction algorithm, we show that even though the shot
noise is still the most significant limiting factors in a realistic survey,
inappropriate treatment of the bias could also shift the reconstructed frame
and therefore broaden the BAO peak. We suggest that, in principle, this
bias-related BAO smearing effect could be used to independently self-calibrate
the bias parameters.
