  Dual-energy CT (DECT) has been increasingly used in imaging applications
because of its capability for material differentiation. However, material
decomposition suffers from magnified noise from two CT images of independent
scans, leading to severe degradation of image quality. Existing algorithms
achieve suboptimal decomposition performance since they fail to accurately
depict the mapping relationship between DECT and the basis material images.
Inspired by the impressive potential of CNN, we developed a new Butterfly
network to perform the image domain dual material decomposition due to its
strong approximation ability to the mapping functions in DECT. The Butterfly
network is derived from the image domain DECT decomposition model by exploring
the geometric relationship between mapping functions of data model and network
components. The network is designed as the double-entry double-out crossover
architecture based on the decomposition formulation. It enters a pair of
dual-energy images as inputs and defines the ground true decomposed images as
each label. The crossover architecture, which plays an important role in
material decomposition, is designed to implement the information exchange
between the two material generation pathways in the network. Network components
exhibit different sensitivity to basis materials in the visualization. By
analyzing their sensitivity to different basis materials, we determined the
roles of network components in material decomposition. This visualization
evaluation reveals what the network can learn and verifies the rationality of
network design. The qualitative and quantitative evaluations in material
decomposition of patient data indicate that the proposed network outperforms
its counterpart.
