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Dual energy CT (DECT) has the potential to decompose tissues into different materials. However, the classic direct inversion (DI) method for multi-material decomposition (MMD) cannot accurately separate more than two basis materials due to the ill-posed problem and amplified image noise. We proposed a novel integrated MMD method that addresses the piecewise smoothness and intrinsic sparsity property of the decomposition image. The proposed MMD was formulated as an optimization problem including a quadratic data fidelity term, an isotropic total variation term that encourages image smoothness, and a non-convex penalty function that promotes decomposition image sparseness. The mass and volume conservation rule were formulated as the probability simplex constraint. An accelerated primal-dual splitting approach with line search was applied to solve the optimization problem. The proposed method with different penalty functions was compared against DI on a digital phantom, a Catphan○c600 phantom, a Quantitative Imaging phantom, and a pelvis patient. The proposed framework distinctly separated the CT image into up to 12 basis materials plus air with high decomposition accuracy. The cross-talks between two different materials are substantially reduced as shown by the decreased non-diagonal elements of the Normalized Cross Correlation (NCC) matrix. The mean square error of the measured electron densities was reduced by 72.6%. Across all datasets, the proposed method improved the average Volume Fraction (VF) accuracy from 63.9% to 99.8% and increased the diagonality of the NCC matrix from 0.73 to 0.96. Compared with DI, the proposed MMD framework improved decomposition accuracy and material separation.
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