Purpose: Dual-energy computed tomography (DECT) is a promising technology that has shown several clinical advantages over conventional x-ray CT, such as improved material identification and artifact suppression. For proton therapy treatment planning, maps of the effective atomic number (Z) and electron density relative to water (ρₑ) can be derived and then employed to improve stopping power ratio (SPR) accuracy and reduce range uncertainty. In this work, we propose a one-step iterative estimation method, which employs multi-domain gradient L₀-norm minimization to reconstruct Z and ρₑ maps.
Methods: The employed gradient L₀-norm is a regularizer that directly and effectively suppresses noise and reduces artifacts in the decomposition domains. In contrast to two-step methods, the investigated optimization model can derive material composition, Z, and ρₑ maps simultaneously. Moreover, we introduce multi-domain regularizers for each search variable. Thus, during the alternative solution process, the noise magnification problem is consistently suppressed. Further, the gradient L₀-norm is superior to traditional Tikhonov and total variation regularizations in sparse representation and edge preservation, which further benefits noise reduction and image fidelity. The algorithm is implemented on a GPU to accelerate the predictive procedure and to support potential real-time adaptive treatment planning.
Results: Both phantom and patient studies demonstrate the superiority of the proposed method in material-selective reconstruction, noise suppression, artifact reduction, and the accurate estimation of ρₑ and Z maps. Moreover, the proposed method can be accelerated by parallel computing so that all the maps are computed in 2 minutes using a single GPU (NVIDIA GeForce GTX 960M).
Conclusion: The proposed one-step iterative estimation method with multi-domain gradient L₀-norm minimization can effectively improve the quality and accuracy of Z and ρₑ maps, which further benefits the SPR calculation for proton therapy and synthesis of monoenergetic images for dose verification or region-of-interest contrast enhancement.