Bayesian joint super-resolution, deconvolution, and denoising of images with Poisson-Gaussian noise

Abstract

For images degraded by significant noise with mixed Poisson-Gaussian (PG) statistics, deconvolution or denoising methods generally do not perform well if they consider only one type of noise. We propose a novel method in a Bayesian framework that simultaneously performs deconvolution, denoising as well as super-resolution, to restore images with mixed PG noise. Our model is based on a likelihood modeling the statistics of PG noise, and a generative Markov random field image prior. We approximate the likelihood using mixtures of Gaussians, which allows defining a block Gibbs sampler for efficient inference. The degraded images are restored through a sampling-based scheme to approximate the Bayesian minimum mean squared error estimate. We have applied our method to different types of synthetic images and real images from a STED microscope. Experiments show that our method can compete with state-of-the-art approaches.