Increasing the Fisher Information Content in the Matter Power Spectrum
  by Non-linear Wavelet Weiner Filtering
  We develop a purely mathematical tool to recover some of the information lost
in the non-linear collapse of large-scale structure. From a set of 141
simulations of dark matter density fields, we construct a non-linear Weiner
filter in order to separate Gaussian and non-Gaussian structure in wavelet
space. We find that the non-Gaussian power is dominant at smaller scales, as
expected from the theory of structure formation, while the Gaussian counterpart
is damped by an order of magnitude on small scales. We find that it is possible
to increase the Fisher information by a factor of three before reaching the
translinear plateau, an effect comparable to other techniques like the linear
reconstruction of the density field.
