Changepoint detection using reversible jump MCMC methods

Abstract

This paper addresses the problem of SAR image segmentation by using reversible jump MCMC sampling.The SAR image segmentation problem is formulated &8 a Bayesian estimation problem. The reversible jump MCMC algorithm is then used to generate samples distributed according to the joint posterior distribution of the unknown parameters.These samples allow to compute marginal maximum a posteriori estimates for the interesting features. The performance of the proposed methodology is illustrated via several simulation results. 1 •. INTRODUCTION The problem of Synthetic Aperture Radar (SAR) image segmentation h&8 received considerable interest in the signal and image processing literature (see for instance (1)[2) and referenCe/! therein). Indeed\ because of the multiplicative speckle noise, most edge. detectors such &8 gradient-based detectors perform poorly· when used for SAR images. This paper studies a new off-line· segmentation algorithm, which operates line-by-line and column-by-column &8 in (3). As explained in [3J, in image segmentation, a retrospective scheme is more attractive as it reflect, the global rather than local aspects 0/ the edge detection problem. The proposed algorithm estimates the number of changepoints, the changepoint locations and the image intensities (usually referred to &8 reflectivities) using a fully Bayesian approach. More precisely, samples distributed according to the a posteriori distribution of the unknown parameters are generated from the reversible jump MCMC algorithm [4). Note that the proposed methodology differs from the off-line procedure studied in [5J. Indeed, instead of generating samples fro� the marginal change location distribution, the proposed MCMC algorithm generates samples· distributed according to the joint distribution of all unknown parameters (i.e. number of changepoints, change locations and image refiectivities). This strategy does not require any marginalization step. As a consequence. the choice of parameter priors is not driven by computational requirements (when nuisance parameters are integrated out. the parameter priers have to be chosen in order to obtain closed form expressions of the interesting marginal distributions). Section 2 formulates the SAR image segmentation problem &8 a Bayesian estimation problem. The likelihood function and the parameter priors necessary to determine the joint posterior distribution of unknown parameters are derived in section 3. Section 4 summarizes the reversible jump MCMC algorithm. which allows to sample from this joint posterior distribution. A simulated annealing algorithm is described in section 5. Simulation results and conclusions are reported in sections 6 and 7.

Bayesian Wideband Spectrum Segmentation for Cognitive Radios

“…The RJMCMC technique has been successfully implemented in a variety of model selection and parameter estimation problems, for example: to determine the number of sinusoids and their parameters in [13], to obtain estimates of the number of scatterers, their directions of arrival and their times of arrival in [14] and to segment SAR images in [15]. When applied to change point detection problems, the algorithm involves 4 "move" types in the sampling process: height and position moves and birth and death moves.…”

Framework for online superimposed event detection by sequential Monte Carlo methods

“…HMM represents the model of the event statistics. MCMCbased methods as in [9,7,10] are generally not applicable in an online approach due to high computational requirements. In [1], an overview of change point detection using particle filters is given.…”