  Dual energy computerized tomography has gained great interest because of its
ability to characterize the chemical composition of a material rather than
simply providing relative attenuation images as in conventional tomography. The
purpose of this paper is to introduce a novel polychromatic dual energy
processing algorithm with an emphasis on detection and characterization of
piecewise constant objects embedded in an unknown, cluttered background.
Physical properties of the objects, specifically the Compton scattering and
photoelectric absorption coefficients, are assumed to be known with some level
of uncertainty. Our approach is based on a level-set representation of the
characteristic function of the object and encompasses a number of
regularization techniques for addressing both the prior information we have
concerning the physical properties of the object as well as fundamental,
physics-based limitations associated with our ability to jointly recover the
Compton scattering and photoelectric absorption properties of the scene. In the
absence of an object with appropriate physical properties, our approach returns
a null characteristic function and thus can be viewed as simultaneously solving
the detection and characterization problems. Unlike the vast majority of
methods which define the level set function non-parametrically, i.e., as a
dense set of pixel values), we define our level set parametrically via radial
basis functions (RBF's) and employ a Gauss-Newton type algorithm for cost
minimization. Numerical results show that the algorithm successfully detects
objects of interest, finds their shape and location, and gives a adequate
reconstruction of the background.
