  Nonlinear gravitational evolution induces strong nonlinearities in the
observed cosmological density fields, leading to positive off-diagonal
correlations in the power spectrum covariance. This has caused the information
saturation in the power spectrum, e.g., the neutrino mass constraints from the
nonlinear power spectra are lower than their linear counterparts by a factor of
$\sim2$ at $z=0$. In this paper, we explore how nonlinear reconstruction
methods improve the cosmological information from nonlinear cosmic fields. By
applying nonlinear reconstruction to cold dark matter fields from the Quijote
simulations, we find that nonlinear reconstruction can improve the constraints
on cosmological parameters significantly, nearly reaching the linear theory
limit. For neutrino mass, the result is only $12\%$ lower than the linear power
spectrum, i.e., the theoretical best result. This makes nonlinear
reconstruction an efficient and useful method to extract neutrino information
from current and upcoming galaxy surveys.
