Unsupervised restoration of subsampled images constructed from geometric and binomial data

In this paper, we investigate a new imaging denoising algorithm for single-photon applications where the classical Poisson noise assumption does not hold. Precisely, we consider two different acquisition scenarios where the unknown intensity profile is to be recovered from subsampled measurements following binomial or geometric distributions, whose parameters are nonlinearly related to the intensities of interest. Adopting a Bayesian approach, a flexible prior model is assigned to the unknown intensity field and an adaptive Markov chain Monte Carlo methods is used to perform Bayesian inference. In particular, it allows us to automatically adjust the amount of regularisation required for satisfactory image inpainting/restoration. The performance of the proposed model/method is assessed quantitatively through a series of experiments conducted with controlled data and the results obtained are very promising for future analysis of multidimensional single-photon images.