An algorithm for constrained one-step inversion of spectral CT data.

Area of Science:

• Medical Imaging
• Computational Science
• Optimization

Background:

• Spectral computed tomography (CT) offers enhanced material differentiation.
• Inverting spectral CT data to basis maps is computationally challenging.
• Existing methods often lack efficient constraint enforcement.

Purpose of the Study:

• To develop a novel primal-dual algorithm for one-step spectral CT inversion.
• To enable the enforcement of image constraints on basis maps during inversion.
• To demonstrate the algorithm's convergence and utility on simulated data.

Main Methods:

• A primal-dual optimization framework was developed.
• Local upper bounding quadratic approximation was used for non-convex terms.
• A new convex-concave optimization strategy was employed.
• The algorithm was tested on simulated spectral CT data with noise and phantoms.

Main Results:

• The algorithm achieves one-step inversion of spectral CT photon counts to basis maps.
• Image constraints can be effectively enforced on the basis maps.
• Convergence was demonstrated on simulated data.
• Successful application shown on noisy data and anthropomorphic phantoms.

Conclusions:

• The developed primal-dual algorithm provides an efficient method for spectral CT data inversion.
• The constrained one-step inversion facilitates improved basis map decomposition.
• This approach holds promise for enhanced spectral CT imaging applications.