Blind Estimation of Reflectivity Profile Under Bayesian Setting Using MCMC Methods

In this paper, we study the problem of inverse electromagnetic scattering to recover multilayer human tissue profiles using ultrawideband radar systems. We pose the recovery problem as a blind deconvolution problem, in which we simultaneously estimate both the transmitted pulse and the underlying dielectric and geometric properties of the one-dimensional tissue profile. We propose comprehensive Bayesian Markov Chain Monte Carlo methods, where the sampler parameters are adaptively updated to maintain desired acceptance ratios. We present the recovery performance of the proposed algorithms on simulated synthetic measurements. We also derive theoretical bounds for the estimation of dielectric properties and provide minimum achievable mean-square-errors for unbiased estimators.