Abstract
OBJECTIVE: Accurate material decomposition is critical for many spectral CT applications. In this work, we introduce a novel framework-spectral diffusion posterior sampling (Spectral DPS)-designed for one-step reconstruction and multi-material decomposition. METHODS: Spectral DPS combines sophisticated prior information captured by one-time unconditional network training and an arbitrary analytic physical system model. Built upon the general DPS framework for nonlinear inverse problems, Spectral DPS incorporates several DPS strategies from our previous work, including jumpstart sampling, Jacobian approximation, and multi-step likelihood updates. The effectiveness of Spectral DPS was evaluated on a simulated dual-layer and a kV-switching spectral system as well as on a physical cone-beam CT (CBCT) test bench. RESULTS: In comparison with other diffusion-based algorithms, Spectral DPS showed significant improvements in reducing sampling variability and computational costs over Baseline DPS. Additionally, Spectral DPS outperformed Conditional Denoising Diffusion Probabilistic Model (DDPM), which was trained on specific imaging conditions, in terms of imaging accuracy and robustness across different imaging protocols. In the physical phantom study, Spectral DPS achieved a $< $1% error in estimating the mean density in a homogeneous region, while effectively avoiding the introduction of false structures seen in Baseline DPS. CONCLUSION: Both simulation and physical phantom studies demonstrated the superior performance of Spectral DPS on accurate, stable, and fast material decomposition. SIGNIFICANCE: Proposed Spectral DPS provided a novel and general material-decomposition framework which can effectively combine learning-based prior and physics-based spectral model. This method can be applied to various spectral CT systems and basis materials.