In this paper we present a novel polychromatic dual energy algorithm with an emphasis on detection of anomalies
whose physical properties are assumed to be known with some level of uncertainty. We assume that material
characteristics are defined by energy independent Compton scatter and photoelectric absorption coefficients.
Uncertainty in material properties are characterized by an elliptical constraint regions in the Compton scatterphotoelectric
coefficient space. We employ an image based iterative reconstruction algorithm to produce images
of Compton scatter and photoelectric absorption coefficients of the medium. The solution is obtained via a nonlinear
optimization process where the prior knowledge about the characteristics of object of interest is imposed
as hard constraints. We also introduce a novel gradient-based similarity regularizer to cope with physics based
limitations on accurately reconstructing the photoelectric absorption coefficient component. Our approach is
based on a parametric level-set representation of the characteristic function of the object. For the reconstruction
of the background we use basis expansion approach using compactly supported exponential radial basis functions.
Numerical results show that the algorithm gives results superior to conventional filtered back projection (FBP)
dual energy method in the presence of noise.