  Astrophysicists are interested in recovering the 3D gas emissivity of a
galaxy cluster from a 2D image taken by a telescope. A blurring phenomenon and
presence of point sources make this inverse problem even harder to solve. The
current state-of-the-art technique is two step: first identify the location of
potential point sources, then mask these locations and deproject the data.
  We instead model the data as a Poisson generalized linear model (involving
blurring, Abel and wavelets operators) regularized by two lasso penalties to
induce sparse wavelet representation and sparse point sources. The amount of
sparsity is controlled by two quantile universal thresholds. As a result, our
method outperforms the existing one.
