Constrained Total Generalized p-Variation Minimization for Few-View X-Ray Computed Tomography Image Reconstruction.

Area of Science:

• Medical Imaging
• Image Reconstruction
• Computational Imaging

Background:

• Total generalized variation (TGV) methods improve CT image reconstruction by preserving edges and reducing staircase artifacts.
• Conventional TGV regularization uses an l1-based form, which is suboptimal for maximizing sparsity priors.

Purpose of the Study:

• To propose a total generalized p-variation (TGpV) regularization model for improved sparsity exploitation in TGV.
• To develop efficient solutions for few-view computed tomography (CT) image reconstruction using the TGpV model.

Main Methods:

• Developed a nonconvex optimization problem for TGpV minimization.
• Presented an iterative algorithm using alternating minimization of an augmented Lagrangian function.
• Utilized variable splitting, generalized p-shrinkage mapping, and proximal point method with fast Fourier transform for efficient solutions.

Main Results:

• The proposed TGpV model effectively exploits sparsity.
• The iterative algorithm provides efficient and explicit solutions to subproblems.
• The method demonstrates accurate and efficient performance on simulated and real data.

Conclusions:

• The proposed TGpV regularization model enhances sparsity exploitation in CT image reconstruction.
• The developed iterative algorithm offers an efficient and feasible solution for few-view CT problems.
• The TGpV method outperforms the standard TGV approach in few-view CT reconstruction.