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, 𝙳𝚊𝚛𝚔𝙼𝚊𝚙𝚙𝚢, and 𝙳𝚎𝚎𝚙𝙼𝚊𝚜𝚜. We use the higher order statistics 𝑀𝑖𝑛𝑘𝑜𝑤𝑠𝑘𝑖 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛𝑎𝑙𝑠 to determine which method best reconstructs the original convergence with efficiency and precision. We find 𝙳𝚎𝚎𝚙𝙼𝚊𝚜𝚜 produces the tightest constraints on cosmological parameters, while Kaiser-Squires, Wiener filter, and 𝙳𝚊𝚛𝚔𝙼𝚊𝚙𝚙𝚢 are similar at a smoothing scale of 3.5 arcmin. We also study the MF inaccuracy caused by inappropriate training sets in the 𝙳𝚎𝚎𝚙𝙼𝚊𝚜𝚜 method and find it to be large compared to the errors, underlining the importance of selecting appropriate training cosmologies.