Spectral CT provides information on material characterization and
quantification because of its ability to separate different basis materials.
Dual-energy (DE) CT provides two sets of measurements at two different source
energies. In principle, two materials can be accurately decomposed from DECT
measurements. However, many clinical and industrial applications require three
or more material images. For triple-material decomposition, a third constraint,
such as volume conservation, mass conservation or both, is required to solve
three sets of unknowns from two sets of measurements. The recently proposed
flexible image-domain (ID) multi-material decomposition (MMD) method assumes
each pixel contains at most three materials out of several possible materials
and decomposes a mixture pixel by pixel. We propose a penalized-likelihood (PL)
method with edge-preserving regularizers for each material to reconstruct
multi-material images using a similar constraint from sinogram data. We develop
an optimization transfer method with a series of pixel-wise separable quadratic
surrogate (PWSQS) functions to monotonically decrease the complicated PL cost
function. The PWSQS algorithm separates pixels to allow simultaneous update of
all pixels, but keeps the basis materials coupled to allow faster convergence
rate than our previous proposed material-and pixel-wise SQS algorithms.
Comparing with the ID method using 2D fan-beam simulations, the PL method
greatly reduced noise, streak and cross-talk artifacts in the reconstructed
basis component images, and achieved much smaller root-mean-square (RMS)
errors.