Multispectral computed tomography (CT) imaging is a crucial tool in modern imaging technology. However, two key challenges exist in conventional multispectral CT image reconstruction: severe beam hardening artifacts and insufficient accuracy in representing the attenuation coefficient. Significant efforts have been made to address these issues, such as the development of photon counting detectors. However, limitations in counting rate and imaging efficiency persist. To enhance the accuracy of attenuation coefficient representation and mitigate these limitations, we propose a multicolor X-ray projection decomposition algorithm.

The proposed algorithm, operating under the constraint of integral invariants, builds upon the theoretical model for multicolor X-ray projection imaging. Unlike conventional approaches, this improved model treats X-ray energy spectrum as an unknown variable. Integral invariant constraints are incorporated into the objective function using the quadratic penalty method, and the Karush-Kuhn-Tucker (KKT) conditions are employed to derive an iterative solution. This allows for the extraction of narrow energy spectrum projections, which are subsequently used to reconstruct narrow spectrum CT images.

To evaluate the efficacy of the proposed model, we assess its ability to reduce beam hardening artifacts and improve the accuracy of the attenuation coefficient. We use the coefficient of variation (CV) as a key metric to measure artifact reduction in narrow energy spectrum images—the lower the CV value, the more effective the artifact removal. In addition, we compare the attenuation coefficients of reconstructed images from the improved model and a baseline model against theoretical reference values. By plotting the results in line graphs, the differences in performance between the models are visually evident. Two test samples are used: 1) a combination of magnesium and aluminum to highlight the model’s capability in distinguishing materials with different attenuation properties; 2) granite, to evaluate the model’s practicality in handling complex materials. The results show that the improved model significantly reduces beam hardening artifacts and produces more accurate attenuation coefficients compared to the baseline model.

The proposed multicolor X-ray projection decomposition algorithm incorporates integral invariant constraints into the theoretical model of multicolor X-ray projection imaging, establishing a new projection decomposition framework. The model is solved by the quadratic penalty function method and KKT conditions, resulting in narrow energy spectrum projections and the subsequent reconstruction of CT images. Experimental results demonstrate that this algorithm provides superior reconstruction quality compared to existing methods, with reduced hardening artifacts, smaller discrepancies in attenuation coefficients, and higher overall accuracy.