  Using higher-order statistics to capture cosmological information from weak
lensing surveys often requires a transformation of observed shear to a
measurement of the convergence signal. This inverse problem is complicated by
noise and boundary effects, and various reconstruction methods have been
developed to implement the process. Here we evaluate the retention of signal
information of four such methods: Kaiser-Squires, Wiener filter,
$\texttt{DarkMappy}$, and $\texttt{DeepMass}$. We use the higher order
statistics $\textit{Minkowski functionals}$ to determine which method best
reconstructs the original convergence with efficiency and precision. We find
$\texttt{DeepMass}$ produces the tightest constraints on cosmological
parameters, while Kaiser-Squires, Wiener filter, and $\texttt{DarkMappy}$ are
similar at a smoothing scale of 3.5 arcmin. We also study the MF inaccuracy
caused by inappropriate training sets in the $\texttt{DeepMass}$ method and
find it to be large compared to the errors, underlining the importance of
selecting appropriate training cosmologies.
