Maximum-likelihood estimation of an astronomical image from a sequence at low photon levels

Abstract

We consider the problem of estimating one nonblurred and cleaned image from a sequence of P randomly translated images corrupted with Poisson noise. We develop a new algorithm based on maximum-likelihood (ML) estimation for two unknown parameters: the reconstructed image itself and the set of translations of the low-light-level images. We demonstrate that the ML reconstructed image is proportional to the sum of the low-light-level images after correcting for the unknown movement and that its entropy is minimal. The images of the sequence are matched together by means of an iterative minimum-entropy algorithm, where a systematic search under displacements for the images is performed. We develop a fast version of this algorithm, and we present results for simulated images and experimental data. The probability of good matching of a low-level image sequence is estimated numerically when the light level of the images in the sequence decreases, corresponding to small numbers of photons detected (down to 20) in each image of the sequence. We compare these results with those obtained when the low-light-level images are matched to a known reference, i.e., the linear correlation method, and with those from the optimal one, when the noise has a Poisson distribution. This approach is applied to astronomical images that are acquired by photocounting from a balloon-borne ultraviolet imaging telescope.