Efficient unsupervised variational Bayesian image reconstruction using a sparse gradient prior

Abstract

In this paper, we present an efficient unsupervised Bayesian approach and a prior distribution adapted to piecewise regular images. This approach is based on a hierarchical prior distribution promoting sparsity on image gradients. It is fully automatic since hyperparameters are estimated jointly with the image of interest. The estimation of all unknowns is performed efficiently thanks to a fast variational Bayesian approximation method. We highlight the good performance of the proposed approach through comparisons with state of the art approaches on an application to a diffraction tomographic problem.