Image-domain multimaterial decomposition for dual-energy computed tomography with nonconvex sparsity regularization

Area of Science:

• Medical Imaging
• Image Processing
• Computational Science

Background:

• Dual-energy computed tomography (CT) enables material decomposition.
• Classic direct inversion (DI) methods struggle with separating more than two materials due to ill-posed problems and noise.
• Accurate multimaterial decomposition (MMD) is crucial for advanced CT applications.

Purpose of the Study:

• To develop an integrated MMD method for dual-energy CT.
• To improve the accuracy and material separation capabilities beyond two basis materials.
• To address limitations of the direct inversion (DI) method.

Main Methods:

• Formulated MMD as an optimization problem incorporating data fidelity, total variation for smoothness, and nonconvex penalties for sparsity.
• Included mass and volume conservation as probability simplex constraints.
• Employed an accelerated primal-dual splitting approach with line search for solving the optimization problem.

Main Results:

• The proposed MMD method successfully separated up to 12 basis materials plus air with high accuracy.
• Significantly reduced cross-talk between materials, evidenced by decreased nondiagonal elements in the normalized cross-correlation (NCC) matrix.
• Achieved a 72.6% reduction in mean square error for electron densities and improved average volume fraction accuracy from 61.2% to 99.9%.

Conclusions:

• The integrated MMD framework offers superior decomposition accuracy and material separation compared to DI.
• The method effectively handles piecewise smoothness and sparsity properties of decomposition images.
• Demonstrated significant improvements in quantitative accuracy and material differentiation in phantom and patient data.