Statistical image‐domain multimaterial decomposition for dual‐energy CT

Purpose: Dual‐energy CT (DECT) enhances tissue characterization because of its basis material decomposition capability. In addition to conventional two‐material decomposition from DECT measurements, multimaterial decomposition (MMD) is required in many clinical applications. To solve the ill‐posed problem of reconstructing multi‐material images from dual‐energy measurements, additional constraints are incorporated into the formulation, including volume and mass conservation and the assumptions that there are at most three materials in each pixel and various material types among pixels. The recently proposed flexible image‐domain MMD method decomposes pixels sequentially into multiple basis materials using a direct inversion scheme which leads to magnified noise in the material images. In this paper, we propose a statistical image‐domain MMD method for DECT to suppress the noise. Methods: The proposed method applies penalized weighted least‐square (PWLS) reconstruction with a negative log‐likelihood term and edge‐preserving regularization for each material. The statistical weight is determined by a data‐based method accounting for the noise variance of high‐ and low‐energy CT images. We apply the optimization transfer principles to design a serial of pixel‐wise separable quadratic surrogates (PWSQS) functions which monotonically decrease the cost function. The separability in each pixel enables the simultaneous update of all pixels. Results: The proposed method is evaluated on a digital phantom, Catphan©600 phantom and three patients (pelvis, head, and thigh). We also implement the direct inversion and low‐pass filtration methods for a comparison purpose. Compared with the direct inversion method, the proposed method reduces noise standard deviation (STD) in soft tissue by 95.35% in the digital phantom study, by 88.01% in the Catphan©600 phantom study, by 92.45% in the pelvis patient study, by 60.21% in the head patient study, and by 81.22% in the thigh patient study, respectively. The overall volume fraction accuracy is improved by around 6.85%. Compared with the low‐pass filtration method, the root‐mean‐square percentage error (RMSE(%)) of electron densities in the Catphan©600 phantom is decreased by 20.89%. As modulation transfer function (MTF) magnitude decreased to 50%, the proposed method increases the spatial resolution by an overall factor of 1.64 on the digital phantom, and 2.16 on the Catphan©600 phantom. The overall volume fraction accuracy is increased by 6.15%. Conclusions: We proposed a statistical image‐domain MMD method using DECT measurements. The method successfully suppresses the magnified noise while faithfully retaining the quantification accuracy and anatomical structure in the decomposed material images. The proposed method is practical and promising for advanced clinical applications using DECT imaging.