Multi-Material Decomposition Using Spectral Diffusion Posterior Sampling

Many spectral CT applications require accurate material decomposition. Existing material decomposition algorithms are often susceptible to significant noise magnification or, in the case of one-step model-based approaches, hampered by slow convergence rates and large computational requirements. In this work, we proposed a novel framework - spectral diffusion posterior sampling (spectral DPS) - for one-step reconstruction and multi-material decomposition, which combines sophisticated prior information captured by one-time unsupervised learning and an arbitrary analytic physical system model. Spectral DPS is built upon a general DPS framework for nonlinear inverse problems. Several strategies developed in previous work, including jumpstart sampling, Jacobian approximation, and multi-step likelihood updates are applied facilitate stable and accurate decompositions. 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. In simulation studies, spectral DPS improved PSNR by 27.49% to 71.93% over baseline DPS and by 26.53% to 57.30% over MBMD, depending on the the region of interest. In physical phantom study, spectral DPS achieved a <1% error in estimating the mean density in a homogeneous region. Compared with baseline DPS, spectral DPS effectively avoided generating false structures in the homogeneous phantom and reduced the variability around edges. Both simulation and physical phantom studies demonstrated the superior performance of spectral DPS for stable and accurate material decomposition.