In this talk, we focus on nonparametric estimators in inverse problems for Poisson processes involving the use of wavelet decompositions. Adopting an adaptive wavelet Galerkin discretization we find that our method combines the well know theoretical advantages of wavelet-vaguelette decompositions for inverse problems in terms of optimally adapting to the unknown smoothness of the solution, together with the remarquably simple closed form expressions of Galerkin inversion methods. Adapting the results of Barron and Sheu to the context of log-intensity functions approximated by wavelet series with the use of the Kullback-Leibler distance between two point processes, we also present an asymptotic analysis of convergence rates that justify our approach. In order to shade some light on the theoretical results obtained and to examine the accuracy of our estimates in finite samples we illustrate our method by the analysis of some simulated examples.