  Massive neutrinos influence the background evolution of the Universe as well
as the growth of structure. Being able to model this effect and constrain the
sum of their masses is one of the key challenges in modern cosmology.
Weak-lensing cosmological constraints will also soon reach higher levels of
precision with next-generation surveys like LSST, WFIRST and Euclid. We use the
MassiveNus simulations to derive constraints on the sum of neutrino masses
$M_{\nu}$, the present-day total matter density $\Omega_{\rm m}$, and the
primordial power spectrum normalization $A_{\rm s}$ in a tomographic setting.
We measure the lensing power spectrum as second-order statistics along with
peak counts as higher-order statistics on lensing convergence maps generated
from the simulations. We investigate the impact of multiscale filtering
approaches on cosmological parameters by employing a starlet (wavelet) filter
and a concatenation of Gaussian filters. In both cases peak counts perform
better than the power spectrum on the set of parameters [$M_{\nu}$,
$\Omega_{\rm m}$, $A_{\rm s}$] respectively by 63$\%$, 40$\%$ and 72$\%$ when
using a starlet filter and by 70$\%$, 40$\%$ and 77$\%$ when using a multiscale
Gaussian. More importantly, we show that when using a multiscale approach,
joining power spectrum and peaks does not add any relevant information over
considering just the peaks alone. While both multiscale filters behave
similarly, we find that with the starlet filter the majority of the information
in the data covariance matrix is encoded in the diagonal elements; this can be
an advantage when inverting the matrix, speeding up the numerical
implementation.
