Blind restoration of linearly degraded discrete signals by Gibbs sampling

This paper addresses the problem of simultaneous parameter estimation and restoration of discrete-valued signals that are blurred by an unknown FIR filter and contaminated by additive Gaussian white noise with unknown variance. Assuming that the signals are stationary Markov chains with known state space but unknown initial and transition probabilities, Bayesian inference of all unknown quantities is made from the blurred and noisy observations. A Monte Carlo procedure, called the Gibbs sampler, is employed to calculate the Bayesian estimates. Simulation results are presented to demonstrate the effectiveness of the method