Perturbation Monte Carlo methods for the solution of inverse problems

We present a computational method that utilizes perturbation Monte Carlo and differential Monte Carlo methods, together with a nonlinear optimization algorithm, to solve inverse problems. Although motivated by biomedical applications, the solution method is quite general and can be applied to inverse problems in other fields. Each such problem involves the use of some form of radiation to probe and identify subtle changes in a complex physical system that is modelled by transport theory.