  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.
