A Bayesian approach to denoising of single-photon binary images

TL;DR

This paper introduces a Bayesian denoising method for single-photon binary images that effectively recovers underlying intensities in photon-limited conditions, outperforming existing techniques.

Contribution

It presents a novel Bayesian framework with a stochastic simulation approach for denoising binary, single-photon images, including analysis of Poisson noise.

Findings

Effective denoising of single-photon binary images

Outperforms state-of-the-art methods on synthetic and real data

Applicable to images with non photon-number resolving detectors

Abstract

This paper discusses new methods for processing images in the photon-limited regime where the number of photons per pixel is binary. We present a new Bayesian denoising method for binary, single-photon images. Each pixel measurement is assumed to follow a Bernoulli distribution whose mean is related by a nonlinear function to the underlying intensity value to be recovered. Adopting a Bayesian approach, we assign the unknown intensity field a smoothness promoting spatial and potentially temporal prior while enforcing the positivity of the intensity. A stochastic simulation method is then used to sample the resulting joint posterior distribution and estimate the unknown intensity, as well as the regularization parameters. We show that this new unsupervised denoising method can also be used to analyze images corrupted by Poisson noise. The proposed algorithm is compared to state-of-the art denoising techniques dedicated to photon-limited images using synthetic and real single-photon measurements. The results presented illustrate the potential benefits of the proposed methodology for photon-limited imaging, in particular with non photonnumber resolving detectors.