Deconvolution of Irregularly Subsampled Images

Imaging technologies, such as coherent fibred bundle optical microscopy (FBOM), operate with irregularly-spaced sparse subsamples from their field of view. In this paper, we address the problem of data deconvolution for applications where the observed irregularly distributed samples are considered as a result of a convolution operator acting on original samples and corrupted by additive observation noise. We propose a hierarchical Bayesian model in which suitable prior distributions are assigned to the unknown model parameters, and compare two estimation strategies including Markov chain Monte Carlo (MCMC) and variational Bayes (VB), which are used to perform Bayesian inference using the posterior distribution. Simulations conducted on both synthetic and real datasets illustrate the benefits of the proposed methods in terms quality of deconvolution of the sparse samples.