Comparing Mass Mapping Reconstruction Methods with Minkowski Functionals

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.