  Reconstruction techniques are commonly used in cosmology to reduce
complicated nonlinear behaviours to a more tractable linearized system. We
study a new reconstruction technique that uses the Moving-Mesh algorithm to
estimate the displacement field from nonlinear matter distribution. We show the
performance of this new technique by quantifying its ability to reconstruct
linear modes. We study the cumulative Fisher information $I(<k_n)$ about the
initial matter power spectrum in the matter power spectra in 130 $N$-body
simulations before and after reconstruction, and find that the nonlinear
plateau of $I(<k_n)$ is increased by a factor of $\sim 50$ after
reconstruction, from $I \simeq 2.5 \times 10^{-5} /({\rm Mpc}/h)^3$ to $I
\simeq 1.3 \times 10^{-3}/({\rm Mpc}/h)^3$ at large $k$. This result includes
the decorrelation between initial and final fields, which has been neglected in
some previous studies. We expect this technique to be beneficial to problems
such as baryonic acoustic oscillations, redshift space distortions and cosmic
neutrinos that rely on accurately disentangling nonlinear evolution from
underlying linear effects.
