  The authors consider the problem of estimating the density $g$ of independent
and identically distributed variables $X\_i$, from a sample $Z\_1, ..., Z\_n$
where $Z\_i=X\_i+\sigma\epsilon\_i$, $i=1, ..., n$, $\epsilon$ is a noise
independent of $X$, with $\sigma\epsilon$ having known distribution. They
present a model selection procedure allowing to construct an adaptive estimator
of $g$ and to find non-asymptotic bounds for its
$\mathbb{L}\_2(\mathbb{R})$-risk. The estimator achieves the minimax rate of
convergence, in most cases where lowers bounds are available. A simulation
study gives an illustration of the good practical performances of the method.
