Transformed Gaussian random fields for unsupervised image deconvolution

This paper deals with the problem of Bayesian deconvolution. Starting from the classical Gaussian Markov Random Fields (GMRF) prior, we present a broader model referred as transformed GMRF (TGRF) in which the latent field results from a nonlinear transformation of a GMRF. We propose a Bayesian inference method to estimate TGRF from an observed image with known parameters, and introduce methods inspired from expectation-maximization in order to jointly deconvolve and estimate the statistical model's parameter for both GMRF and TGRF. Numerical results allow to determine the best inference method among several possibilities on fully synthetic data, on a phantom image and on real fluorescence microscopy images.