Bayesian Parameter Estimation for Electromagnetic Inverse Scattering using Contrast Source Inversion and Hamiltonian Monte Carlo

In the traditional approach to electromagnetic inverse scattering problems, we seek a single reconstruction of the dielectric properties using knowledge of transmitted signals and the measured scattered electric field. The Bayesian approach to the problem desires information regarding the posterior distribution of the dielectric properties given the data. The benefits of Bayesian parameter estimation include the ability to quantify uncertainty of any point estimation chosen from the posterior distribution, as well as a more flexible and intuitive approach concerning the injection of prior information into the inversion scheme. However, in most practical problems we are unable to analytically specify the posterior distribution and must instead rely on techniques such as Markov chain Monte Carlo (MCMC) in order to produce estimates of any desired reconstruction statistics. These MCMC methods are often computationally intensive, and can be prohibitively expensive for nonlinear inversion techniques in which the dimension of the parameter space is large and multiple solutions of the forward scattering problem are required at each iteration.