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In this investigation, we propose several algorithms to recover the locationand intensity of a radiation source located in a simulated 250 m x 180 m blockin an urban center based on synthetic measurements. Radioactive decay anddetection are Poisson random processes, so we employ likelihood functions basedon this distribution. Due to the domain geometry and the proposed responsemodel, the negative logarithm of the likelihood is only piecewise continuousdifferentiable, and it has multiple local minima. To address thesedifficulties, we investigate three hybrid algorithms comprised of mixedoptimization techniques. For global optimization, we consider SimulatedAnnealing (SA), Particle Swarm (PS) and Genetic Algorithm (GA), which relysolely on objective function evaluations; i.e., they do not evaluate thegradient in the objective function. By employing early stopping criteria forthe global optimization methods, a pseudo-optimum point is obtained. This issubsequently utilized as the initial value by the deterministic ImplicitFiltering method (IF), which is able to find local extrema in non-smoothfunctions, to finish the search in a narrow domain. These new hybrid techniquescombining global optimization and Implicit Filtering address difficultiesassociated with the non-smooth response, and their performances are shown tosignificantly decrease the computational time over the global optimizationmethods alone. To quantify uncertainties associated with the source locationand intensity, we employ the Delayed Rejection Adaptive Metropolis (DRAM) andDiffeRential Evolution Adaptive Metropolis (DREAM) algorithms. Marginaldensities of the source properties are obtained, and the means of the chains'compare accurately with the estimates produced by the hybrid algorithms.

Hybrid optimization and Bayesian inference techniques for a non-smooth radiation detection problem