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Many clinical applications depend critically on the accurate differentiation and classification of different types of materials in patient anatomy. This work introduces a unified framework for accurate nonlinear material decomposition and applies it, for the first time, in the concept of triple-energy CT (TECT) for enhanced material differentiation and classification as well as dual-energy CT (DECT).We express polychromatic projection into a linear combination of line integrals of material-selective images. The material decomposition is then turned into a problem of minimizing the least-squares difference between measured and estimated CT projections. The optimization problem is solved iteratively by updating the line integrals. The proposed technique is evaluated by using several numerical phantom measurements under different scanning protocols. The triple-energy data acquisition is implemented at the scales of micro-CT and clinical CT imaging with commercial “TwinBeam” dual-source DECT configuration and a fast kV switching DECT configuration. Material decomposition and quantitative comparison with a photon counting detector and with the presence of a bow-tie filter are also performed.The proposed method provides quantitative material- and energy-selective images examining realistic configurations for both DECT and TECT measurements. Compared to the polychromatic kV CT images, virtual monochromatic images show superior image quality. For the mouse phantom, quantitative measurements show that the differences between gadodiamide and iodine concentrations obtained using TECT and idealized photon counting CT (PCCT) are smaller than 8 and 1 mg/mL, respectively. TECT outperforms DECT for multicontrast CT imaging and is robust with respect to spectrum estimation. For the thorax phantom, the differences between the concentrations of the contrast map and the corresponding true reference values are smaller than 7 mg/mL for all of the realistic configurations.A unified framework for both DECT and TECT imaging has been established for the accurate extraction of material compositions using currently available commercial DECT configurations. The novel technique is promising to provide an urgently needed solution for several CT-based diagnostic and therapy applications, especially for the diagnosis of cardiovascular and abdominal diseases where multicontrast imaging is involved.