Purpose: Dual-Energy Computed Tomography (DECT) is of great interest in medical imaging, security inspection, and nondestructive testing. Most DECT reconstruction methods focus on producing two material images with different linear attenuation coefficients. However, the ability to reconstruct three or more basis materials is clinically and industrially important. Under the assumption that there are at most three materials in each pixel, there are a few methods that estimate multiple material images from DECT measurements by enforcing sum-to-one and a box constraint ([0 1]) derived from both the volume and mass conservation assumption. The recently proposed image-domain multimaterial decomposition (MMD) method introduces edge-preserving regularization for each material image. It enforces the assumption that there are at most three materials in each pixel using a time-consuming loop over all possible material triplets. However, this method neglects relations among material images. We propose a new image-domain MMD model for DECT that considers the prior information that different material images have common or complementary edges and encourages sparsity of material composition in each pixel using regularization.
Method: The proposed PWLS-TNV-ℓ0 method uses penalized weighted least-square (PWLS) reconstruction with three regularization terms. The first term is total nuclear variation (TNV) that accounts for the image property that basis material images share common or complementary boundaries and each material image is piecewise constant. The second term is an ℓ0 norm that encourages each pixel containing a small subset of material types out of several possible materials. The third term is a characteristic function based on sum-to-one and a box constraint derived from the volume and mass conservation assumption. We apply the Alternating Direction Method of Multipliers (ADMM) to optimize the cost function of the PWLS-TNV-ℓ0 method.
Result: We evaluated the proposed method on a simulated digital phantom, Catphan©600 phantom and patient's pelvis data. We implemented two existing image-domain MMD methods for DECT, the Direct Inversion and the PWLS-EP-LOOP method. We initialized the PWLS-TNV-ℓ0 method and the PWLS-EP-LOOP method with the results of the Direct Inversion method and compared performance of the proposed method with that of the PWLS-EP-LOOP method. The proposed method lowers the bias of decomposed material fractions by 84.47% in the digital phantom study, by 99.50% in the Catphan©600 phantom study, and by 99.64% in the pelvis patient study, respectively, compared to the PWLS-EP-LOOP method. The proposed method reduces noise standard deviation (STD) by 52.21% in the Catphan©600 phantom study, and by 16.74% in the patient's pelvis study, compared to the PWLS-EP-LOOP method. The proposed method increases volume fraction accuracy by 6.04%,20.55%, and 13.46% for the digital phantom, the Catphan©600 phantom, and the patient's pelvis study, respectively, compared to the PWLS-EP-LOOP method. Compared with the PWLS-EP-LOOP method, the root mean square percentage error [RMSE(%)] of electron densities in the Catphan©600 phantom is decreased by about 7.39%.
Conclusions: We proposed an image-domain MMD method, PWLS-TNV-ℓ0 , for DECT. The PWLS-TNV-ℓ0 method takes low rank property of material image gradients, sparsity of material composition and mass and volume conservation into consideration. The proposed method suppresses noise, reduces cross contamination, and improves accuracy in the decomposed material images, compared to the PWLS-EP-LOOP method.
Keywords: dual-energy CT (DECT); multimaterial decomposition (MMD); penalized weighted least-square (PWLS); spectral CT; total nuclear variation (TNV).
© 2018 American Association of Physicists in Medicine.