Reconstruction of astronomical images from low-photon image sequence: study for Gaussian displacements

In the restoration of images from low photon-level data, an estimate of the reconstructed image is often carried out in the general framework of Bayesian statistical estimation. We have developed a new method (Guillaume et al. 1998) for image reconstruction from a sequence of low photon-level and translated astronomical images. We research the maximum a posteriori estimate of the translations to reconstruct a clean image, for data described by a Poisson law. We present results obtained with an optimal algorithm for random, Gaussian and correlated or non-correlated displacements of the images, and we show that taking into account the displacements' nature can improve results.