Multi-energy, Limited View Computed Tomography (CT)
The development of energy selective photon counting detectors (PCDs) for X-ray computed tomography has created the possibility for significantly enhancing the materials characterization capabilities relative to existing dual energy systems that seek to recover material density and effective atomic number (or equivalently, spatial maps of Compton and photoelectric coefficients). Because of the overlapping nature of these spectra, a characteristic of all fielded dual energy systems, as well as the nature of X-ray physics, it is well known that stable recovery of atomic number is very difficult. Moreover, the two dimensional density/atomic number “feature space” is also known to be insufficient for reliably discriminating many modern explosives from non-threat objects. By moving to a multi- or hyper-spectral form of CT, where data are acquired over narrow energy ranges, we gain the ability to recover material absorption as a function of three spatial dimensions and energy. Thus, at each voxel in the reconstruction we will possess not two parameters to characterize the material, but the full spectral response of the material. We hypothesize that this much-enhanced, physics-based feature space will significantly improve our ability to identify threat materials, even in cluttered environments. The work we are proposing represents the enabling algorithmic technology, which will allow future multi-energy systems to meet the needs of DHS.
Previously we have developed iterative reconstruction methods based on a treatment of the absorption as a tensor; that is a mathematical object defined in three (two space and one energy) or four (three space and one energy) dimensions. A tensor model, for the unknown, is very much the natural way of dealing with the inherent structure of this quantity as a function of both space and energy. When limited data are available, the problem is ill-posed so that regularization is required. Recently, there has been significant interest in “sparsifying” methods to aid in the solution of problems such as this. Our efforts in extending these ideas from the image to the tensor domain for X-ray tomography have been promising. Relative to existing state-of-the-art ideas for iterative X-ray reconstruction using total variation (TV) regularization on an energy-by energy basis, our approach yields significantly reduced mean square error, especially at the lower energies. Moreover, initial evidence suggests that our tensor method is better able to recover texture. As it is widely acknowledged that texture in a CT reconstruction may be an important feature for identifying many modern threat materials, we anticipate that this work may have direct relevance to this challenging and important problem.