J. Tachella, Y. Altmann, M. Pereyra, J-.Y. Tourneret and S. McLaughlin
Status: Accepted for publication on European Conference on Signal Processing (EUSIPCO), Rome, 2018.
This paper investigates different algorithms to perform image restoration from single-photon measurements corrupted with Poisson noise. The restoration problem is formulated in a Bayesian framework and several state-of-the-art Monte Carlo samplers are considered to estimate the unknown image and quantify its uncertainty. The different samplers are compared through a series of experiments conducted with synthetic images. The results demonstrate the scaling properties of the proposed samplers as the dimensionality of the problem increases and the number of photons decreases. Moreover, our experiments show that for a certain photon budget (i.e., acquisition time of the imaging device), downsampling the observations can yield better reconstruction results.