  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.
