Sub-pixel image registration with a maximum likelihood estimator. Application to the first adaptive optics observations of Arp 220 in the L' band

We present a new method based on a maximum likelihood (ML) estimation of the sub-pixel shift between images of a given object observed with a single instrument. We first study the case of two noisy images and give the ML approach of the registration problem. By means of simulations, we show the gain obtained with this ML solution compared to a classical registration method with an academic noise model (stationary white Gaussian), and then demonstrate the relevance of this ML estimation with a more realistic noise model. We then address the problem of a sequence of low signal frames of the same object. We develop a joint ML approach in which we simultaneously estimate the reference (i.e. the noiseless) image and the shift parameters. The registration accuracy is increased at low photon levels as the number of frames grows, reaching the sub-pixel domain at very low SNR (about 1), when considering 100 frames. When applied to experimental data (thermal IR images of a faint galaxy), both ML methods show their efficiency to recover the resolution in averaged frames and totally outperform the classical cross-correlation.