Bayesian Segmentation in Signal with Multiplicative Noise Using Reversible Jump MCMC

Abstract

This paper proposes the important issues in signal segmentation. The signal is disturbed by multiplicative noise where the number of segments is unknown. A Bayesian approach is proposed to estimate the parameter. The parameter includes the number of segments, the location of the segment, and the amplitude. The posterior distribution for the parameter does not have a simple equation so that the Bayes estimator is not easily determined. Reversible Jump Markov chain Monte Carlo (MCMC) method is adopted to overcome the problem. The Reversible Jump MCMC method creates a Markov chain whose distribution is close to the posterior distribution. The performance of the algorithm is shown by simulation data. The result of this simulation shows that the algorithm works well. As an application, the algorithm is used to segment a Synthetic Aperture Radar (SAR) signal. The advantage of this method is that the number of segments, the position of the segment change, and the amplitude are estimated simultaneously.