When dealing with material classification in baggage at airports, Dual-Energy Computed Tomography (DECT) allows characterization of any given material with coefficients based on two attenuative effects: Compton scattering and photoelectric absorption. However, straightforward projection-domain decomposition methods for this characterization often yield poor reconstructions due to the high dynamic range of material properties encountered in an actual luggage scan. Hence, for better reconstruction quality under a timing constraint, we propose a splitting-based, GPU-accelerated, statistical DECT reconstruction algorithm. Compared to prior art, our main contribution lies in the significant acceleration made possible by separating reconstruction and decomposition within an Alternating Direction Method of Multipliers (ADMM) framework. Experimental results, on both synthetic and real-world baggage phantoms, demonstrate a significant reduction in time required for convergence.