Gaussianizing the non-Gaussian lensing convergence field I: the
  performance of the Gaussianization
  Motivated by recent works of Neyrinck et al. 2009 and Scherrer et al. 2010,
we proposed a Gaussianization transform to Gaussianize the non-Gaussian lensing
convergence field $\kappa$. It performs a local monotonic transformation
$\kappa\rightarrow y$ pixel by pixel to make the unsmoothed one-point
probability distribution function of the new variable $y$ Gaussian. We tested
whether the whole $y$ field is Gaussian against N-body simulations. (1) We
found that the proposed Gaussianization suppresses the non-Gaussianity by
orders of magnitude, in measures of the skewness, the kurtosis, the 5th- and
6th-order cumulants of the $y$ field smoothed over various angular scales
relative to that of the corresponding smoothed $\kappa$ field. The residual
non-Gaussianities are often consistent with zero within the statistical errors.
(2) The Gaussianization significantly suppresses the bispectrum. Furthermore,
the residual scatters around zero, depending on the configuration in the
Fourier space. (3) The Gaussianization works with even better performance for
the 2D fields of the matter density projected over $\sim 300 \mpch$ distance
interval centered at $z\in(0,2)$, which can be reconstructed from the weak
lensing tomography. (4) We identified imperfectness and complexities of the
proposed Gaussianization. We noticed weak residual non-Gaussianity in the $y$
field. We verified the widely used logarithmic transformation as a good
approximation to the Gaussianization transformation. However, we also found
noticeable deviations.
