Bayesian detection of signal under Rayleigh multiplicative noise based on reversible jump MCMC

Abstract

Piecewise constant models have been used in signal processing. The signal contains noise so noise needs to be eliminated. Several research results have used the assumption that noise has a normal, gamma, or Laplace distribution. However, the signal may have noise with other distributions. This study aims to propose a piecewise-constant model in which noise is assumed to have a Rayleigh distribution. This study also proposes a method for estimating the parameters of a piecewise-constant model that contains Rayleigh noise. The parameters of the piecewise constant model were estimated in the Bayesian framework by adopting the reversible jump Markov Chain Monte Carlo (MCMC) method. This research shows that the dimension of the parameter space is a combination of several spaces with different dimensions. Bayes estimators for the parameters of the piecewise constant model cannot be stated explicitly. The reversible jump MCMC method is used to calculate the Bayes estimator. The results of this study have a significant contribution in providing Rayleigh noise as an alternative noise in signal processing. This research has a novelty, namely: the use of Rayleigh noise in the piecewise constant model and the hierarchical Bayesian procedure to estimate the parameters of the piecewise constant model. Further research can be extended to the estimation procedure of the piecewise constant with Weibull noise.