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We propose a deconvolution algorithm for images blurred and degraded by a Poisson noise. The algorithm uses a fast proximal backward-forward splitting iteration. This iteration minimizes an energy which combines a non-linear data fidelity term, adapted to Poisson noise, and a non- smooth sparsity-promoting regularization (e.g lscr1-norm) over the image representation coefficients in some dictionary of transforms (e.g. wavelets, curvelets). Our results on simulated microscopy images of neurons and cells are confronted to some state-of-the-art algorithms. They show that our approach is very competitive, and as expected, the importance of the non-linearity due to Poisson noise is more salient at low and medium intensities. Finally an experiment on real fluorescent confocal microscopy data is reported.