Unified Projection-Domain Material Decomposition for Energy-Integrating and Photon-Counting CT
Objective: To develop a unified and efficient method for projection-domain material decomposition in spectral computed tomography (CT) that incorporates an arbitrary number of spectral measurements, independent of the acquisition mechanism, without reducing the measurements to two effective energies. Approach: A nested optimization method was developed for two-material basis decomposition from K>=2 spectral measurements. It extends an existing two-measurement univariate method by replacing its polynomial approximation with profile minimization of the Poisson negative log-likelihood, reducing the inversion to two one-dimensional searches that use all measurements without spectral rebinning. The method was evaluated in simulation for energy-integrating (GE Revolution Apex Elite, Siemens SOMATOM Flash) and photon-counting (Siemens NAEOTOM Alpha) CT. Main results: The method recovered line integrals with noiseless iodine errors below 3e-6 g/cm^2 and noise within 3% of the Cramer-Rao lower bound (CRLB). Virtual monoenergetic images (VMIs) agreed, at 70 keV and above, with reference CT numbers and, on all three systems, with vendor VMIs of physical scans (mean absolute error 6-22 HU). For photon counting, four measurements instead of two reduced the iodine CRLB by 19% and image noise by 8-16% at every VMI energy, and lowered the regression error at 70 keV and above. Iteration and tolerance settings changed CT numbers by less than 0.04 HU, and decomposition took 0.34-0.67 s per million rays on an A100 GPU. Significance: The method provides fast, accurate decomposition for any spectral CT acquisition mechanism and number of measurements, so one method can serve every scanner in a virtual imaging trial.