Monte Carlo Approach: Gibbs Sampling

Monte Carlo methods have been used in a wide range of problems in signal and image processing. One of the most commonly used methods is the Gibbs sampler, a Monte Carlo Markov chain (MCMC) algorithm that is used to generate samples from a multivariate p.d.f. that is difficult to sample directly. The Gibbs sampler can be considered as a specialized form of the Metropolis–Hastings algorithm. The latter aims to set up a Markov chain whose distribution converges to the desired target distribution. This chapter explains the casting of the sparse image reconstruction problem in the Bayesian framework. MAP estimate using the Gibbs sampler and uncertainty in the blur point spread function are discussed. A simulation example illustrates the proposed sparse reconstructor.