  Dual Energy Cone Beam Computed Tomography (DE-CBCT) is a promising technique
for several medical applications, including dynamic angiography. Recently, a
dynamical two-step method has been proposed : first, the water and iodine
projections are computed from the multi-energy sinograms, then, a dynamic image
of the iodine contrast is reconstructed using 4D Total-Variation (TV)
constrained reconstruction from the iodine projections. In contrast to the
2-step methods, one-step methods use a model relating directly the
multi-material images to the multi-energy sinograms. This kind of methods are
well-known to reduce the noise correlation between the material images by
avoiding the intermediate decomposition step, but request to solve an
non-convex large scale optimization problem which can be challenging. In this
work we use the Non-Linear Primal-Dual Hybrid Gradient Method (NL-PDHGM)
optimization framework to propose two versions of a one-step method which is
based on an empirical model : the first one is a version which considers the
multi-material images as static object whereas the second version is developped
for a specific application with a static water image and a dynamic iodine image
consisting of a series of 3D iodine images associated to different time points.
This last version is developped to obtain the evolution of the iodine
concentration in the blood vessels during a single CBCT scan. To evaluate the
proposed one-step methods we used simulations which consider a CBCT system with
dual layer spectral detector and a brain phantom with a static and a dynamic
vascular tree. The proposed one-step methods are compared with 2-step methods.
