Adaptive optimization framework for accurate multi-material decomposition in dual-energy CT

<i>Purpose</i>. This study introduces an Adaptive Optimization-based Multi-Material Decomposition with Total Nuclear Variation (AO-MMD-TNV) for dual-energy CT (DECT), designed to achieve accurate and noise-robust material fraction estimation.<i>Methods</i>. Three experimental datasets-a digital phantom, a tissue characterization phantom, and a human-shaped phantom-were used to evaluate the proposed method. The algorithm combines a robust Huber data term, iteratively reweighted L1 sparsity, and Total Nuclear Variation (TNV) regularization under simplex constraints. Adaptive weighting was applied to balance physical fidelity, sparsity, and boundary coherence. The performance was quantitatively compared with a conventional triplet-based MMD approach using metrics of volume fraction accuracy (VFA) and standard deviation (STD).<i>Results</i>. The AO-MMD-TNV achieved 100% VFA for all five materials in the digital phantom, with complete noise suppression (STD = 0). In the tissue characterization phantom, the method demonstrated improved VFA in most ROIs, though minor accuracy reductions were observed for breast and solid water (ROIs 3 and 4) due to their similar attenuation to background. In the human-shaped phantom, the AO-MMD-TNV maintained stable performance across six organ-related ROIs, outperforming MMD in quantitative consistency and noise robustness.<i>Conclusions</i>. The proposed AO-MMD-TNV framework effectively enhances quantitative reliability, reduces noise and crosstalk, and preserves anatomical boundaries. While further optimization is needed for low-contrast materials, AO-MMD-TNV demonstrates strong potential for precise, physically consistent DECT-based material quantification and clinical application.