Efficient TpV minimization for circular, cone-beam computed tomography reconstruction via non-convex optimization.

Area of Science:

• Medical imaging
• Computational imaging
• Image reconstruction

Background:

• Current methods for volume image reconstruction from cone-beam scans often use L1 norm of gradient magnitude images (GMI) for total variation regularization.
• This approach may not optimally capture the sparsity of GMI, potentially limiting reconstruction accuracy.

Purpose of the Study:

• To propose an efficient iterative algorithm for volume image reconstruction from circular cone-beam scans.
• To introduce a generalized total p-variation (TpV) minimization model using a p-shrinkage-induced penalty function for improved sparsity measurement of GMI.

Main Methods:

• Development of a reconstruction model using generalized total p-variation (TpV) minimization with non-negativity constraints.
• Application of the alternating direction minimization (ADM) scheme to solve the constrained optimization problem, leveraging the closed-form expression of the proximal mapping for p-shrinkage penalties.
• Efficient implementation of the algorithm, named "TpV-ADM," utilizing graphics processing units (GPUs).

Main Results:

• The proposed "TpV-ADM" algorithm demonstrates efficient and stable volume image reconstruction.
• The method proves robust and accurate, particularly for datasets with very few views.
• Verification across ideal, noisy, and real projection datasets confirms the effectiveness of the TpV-ADM approach.

Conclusions:

• The generalized total p-variation (TpV) minimization model and the associated ADM algorithm offer a promising advancement in cone-beam CT reconstruction.
• The TpV-ADM method provides superior sparsity measurement and reconstruction performance compared to conventional techniques, especially in low-view scenarios.