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Image Reconstruction in Cone Beam Computed Tomography Using Controlled Gradient Sparsity

Alexander Meaney, Mikael A. K. Brix, Miika T. Nieminen, Samuli Siltanen

TL;DR

This work addresses CBCT reconstruction under challenging conditions (e.g., low-dose, sparse-view) by integrating total variation regularization with an adaptive scheme that targets a predefined gradient sparsity. It employs a normalized forward model and a primal-dual fixed-point (PDFP) solver, augmented by a control-theoretic update of the regularization parameter to drive the gradient sparsity toward a specified level $\mathcal{C}_{pr}$. The key contributions are the automatic regularization control via $\mathcal{C}_{\nabla f}$, improved interpretability of the regularization strength, and a GPU-accelerated 3D reconstruction framework demonstrated on simulated data with clinically feasible runtimes. This approach has potential to enable robust, dose-efficient CBCT reconstructions with reduced artifacts and enhanced feature visibility in practice.

Abstract

Total variation (TV) regularization is a popular reconstruction method for ill-posed imaging problems, and particularly useful for applications with piecewise constant targets. However, using TV for medical cone-beam computed X-ray tomography (CBCT) has been limited so far, mainly due to heavy computational loads at clinically relevant 3D resolutions and the difficulty in choosing the regularization parameter. Here an efficient minimization algorithm is presented, combined with a dynamic parameter adjustment based on control theory. The result is a fully automatic 3D reconstruction method running in clinically acceptable time. The input on top of projection data and system geometry is desired degree of sparsity of the reconstruction. This can be determined from an atlas of CT scans, or alternatively used as an easily adjustable parameter with straightforward interpretation.

Image Reconstruction in Cone Beam Computed Tomography Using Controlled Gradient Sparsity

TL;DR

This work addresses CBCT reconstruction under challenging conditions (e.g., low-dose, sparse-view) by integrating total variation regularization with an adaptive scheme that targets a predefined gradient sparsity. It employs a normalized forward model and a primal-dual fixed-point (PDFP) solver, augmented by a control-theoretic update of the regularization parameter to drive the gradient sparsity toward a specified level . The key contributions are the automatic regularization control via , improved interpretability of the regularization strength, and a GPU-accelerated 3D reconstruction framework demonstrated on simulated data with clinically feasible runtimes. This approach has potential to enable robust, dose-efficient CBCT reconstructions with reduced artifacts and enhanced feature visibility in practice.

Abstract

Total variation (TV) regularization is a popular reconstruction method for ill-posed imaging problems, and particularly useful for applications with piecewise constant targets. However, using TV for medical cone-beam computed X-ray tomography (CBCT) has been limited so far, mainly due to heavy computational loads at clinically relevant 3D resolutions and the difficulty in choosing the regularization parameter. Here an efficient minimization algorithm is presented, combined with a dynamic parameter adjustment based on control theory. The result is a fully automatic 3D reconstruction method running in clinically acceptable time. The input on top of projection data and system geometry is desired degree of sparsity of the reconstruction. This can be determined from an atlas of CT scans, or alternatively used as an easily adjustable parameter with straightforward interpretation.

Paper Structure

This paper contains 11 sections, 24 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Methods
  3. CBCT Imaging Model
  4. Total Variation Regularization
  5. Controlled Gradient Sparsity
  6. Dose and Noise Considerations
  7. Computational Implementation
  8. Experiments Using Simulated Data
  9. Results
  10. Simulated data
  11. Discussion

Figures (4)

  • Figure 1: Convergence of the relative distance between consecutive TV-CGS iterations for the 3D Shepp-Logan phantom when $N_1 = N_2 = N_3 = 256$ and $I_0 = 1000$.
  • Figure 2: Convergence of a) $\mathcal{C}_{\nabla f}$, and b) $\alpha$ for the 3D Shepp-Logan phantom when $N_1 = N_2 = N_3 = 256$ and $I_0 = 1000$.
  • Figure 3: Center slices in the axial, coronal, and sagittal directions of the ground truth, the FDK reconstruction, and the TV-CGS reconstruction with $I_0 = 1000$ and $\mathcal{C}_\mathrm{pr} = 0.15$.
  • Figure 4: Convergence of a) $\mathcal{C}_{\nabla f}$, and b) $\alpha$ for the 3D Shepp-Logan phantom when $N_1 = N_2 = N_3 = 256$ and $\mathcal{C}_\mathrm{pr} = 0.15$.