Light on Dark Matter with Weak Gravitational Lensing
  This paper reviews statistical methods recently developed to reconstruct and
analyze dark matter mass maps from weak lensing observations. The field of weak
lensing is motivated by the observations made in the last decades showing that
the visible matter represents only about 4-5% of the Universe, the rest being
dark. The Universe is now thought to be mostly composed by an invisible,
pressureless matter -potentially relic from higher energy theories- called
"dark matter" (20-21%) and by an even more mysterious term, described in
Einstein equations as a vacuum energy density, called "dark energy" (70%). This
"dark" Universe is not well described or even understood, so this point could
be the next breakthrough in cosmology. Weak gravitational lensing is believed
to be the most promising tool to understand the nature of dark matter and to
constrain the cosmological model used to describe the Universe. Gravitational
lensing is the process in which light from distant galaxies is bent by the
gravity of intervening mass in the Universe as it travels towards us. This
bending causes the image of background galaxies to appear slightly distorted
and can be used to extract significant results for cosmology. Future weak
lensing surveys are already planned in order to cover a large fraction of the
sky with large accuracy. However this increased accuracy also places greater
demands on the methods used to extract the available information. In this
paper, we will first describe the important steps of the weak lensing
processing to reconstruct the dark matter distribution from shear estimation.
Then we will discuss the problem of statistical estimation in order to set
constraints on the cosmological model. We review the methods which are
currently used especially new methods based on sparsity.
