Perfect sampling: a review and applications to signal processing

Markov chain Monte Carlo (MCMC) sampling methods have gained much popularity among researchers in signal processing. The Gibbs and the Metropolis-Hastings (1954, 1970) algorithms, which are the two most popular MCMC methods, have already been employed in resolving a wide variety of signal processing problems. A drawback of these algorithms is that in general, they cannot guarantee that the samples are drawn exactly from a target distribution. New Markov chain-based methods have been proposed, and they produce samples that are guaranteed to come from the desired distribution. They are referred to as perfect samplers. We review some of them, with the emphasis being given to the algorithm coupling from the past (CFTP). We also provide two signal processing examples where we apply perfect sampling. In the first, we use perfect sampling for restoration of binary images and, in the second, for multiuser detection of CDMA signals