The authors consider the problem of estimating the density $g$ of independent and identically distributed variables $X_i$, from a sample $Z_1, \dots, Z_n$ where $Z_i=X_i+\sigma\varepsilon_i$, $i=1, \dots, n$, $\varepsilon$ is a noise independent of $X$, with $\sigma\varepsilon$ 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.