Modeling the effect of massive neutrinos on the background evolution of the Universe and the growth of structure is one of the key challenges in modern cosmology. Weak-lensing cosmological constraints will also soon reach higher levels of precision with next-generation galaxy surveys. To extract the non-Gaussian cosmological information encoded in cosmic shear data, weak lensing peak counts have proven to be a powerful tool. In this talk, I present the advantages of multi-scale filtering techniques when performing inference on cosmological parameters with peak counts computed on simulated weak lensing convergence maps as input data. To illustrate this, I will show the impact on cosmological constraints of a starlet filter and a multi-Gaussian filter applied on noisy convergence maps generated from the Cosmological Massive Neutrino Simulations (MassiveNuS) when employing the lensing power spectrum and peak counts as summary statistics.