We present advances in inverse transport methods and demonstrate their application to neutron tomography problems that have significant scattering. The problem we consider is inference of the material distribution in an object by detection and analysis of the radiation exiting from it. Our approach combines both deterministic and stochastic optimization methods to find a material distribution that minimizes the difference between computed and measured detector responses. The main advances are dimension-reduction schemes that we have designed to take advantage of known and postulated constraints. One key constraint is that the cross sections for a given region in the object must be the cross sections for a real material. We illustrate our approach using a neutron tomography model problem on which we impose reasonable constraints, similar to those that in practice would come from prior information or engineering judgment. This problem shows that our method is capable of generating results that are much better than those of deterministic minimization methods and dramatically more efficient than those of typical stochastic methods.
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