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Integer Optimization of CT Trajectories using a Discrete Data Completeness Formulation

Linda-Sophie Schneider, Gabriel Herl, Andreas Maier

TL;DR

Addressing data completeness in CT with twin robotic trajectories, the paper introduces a discrete data completeness formulation and an IP-based projection-selection method to pick $k$ viewing directions that maximize Radon-space coverage. It samples the unit sphere around VOIs and uses an absorption-based reliability metric $A_D$, solved via a branch-and-cutIP with an optimality gap as a quality measure. Empirical results compare against equidistant circular and greedy strategies, showing higher SSIM and PSNR and greater coverage (e.g., up to ~91% in some cases) with IP. The approach enables automated, data-complete trajectory design for complex objects and resource-constrained scans, with potential to reduce scan times and artifacts.

Abstract

X-ray computed tomography (CT) plays a key role in digitizing three-dimensional structures for a wide range of medical and industrial applications. Traditional CT systems often rely on standard circular and helical scan trajectories, which may not be optimal for challenging scenarios involving large objects, complex structures, or resource constraints. In response to these challenges, we are exploring the potential of twin robotic CT systems, which offer the flexibility to acquire projections from arbitrary views around the object of interest. Ensuring complete and mathematically sound reconstructions becomes critical in such systems. In this work, we present an integer programming-based CT trajectory optimization method. Utilizing discrete data completeness conditions, we formulate an optimization problem to select an optimized set of projections. This approach enforces data completeness and considers absorption-based metrics for reliability evaluation. We compare our method with an equidistant circular CT trajectory and a greedy approach. While greedy already performs well in some cases, we provide a way to improve greedy-based projection selection using an integer optimization approach. Our approach improves CT trajectories and quantifies the optimality of the solution in terms of an optimality gap.

Integer Optimization of CT Trajectories using a Discrete Data Completeness Formulation

TL;DR

Addressing data completeness in CT with twin robotic trajectories, the paper introduces a discrete data completeness formulation and an IP-based projection-selection method to pick viewing directions that maximize Radon-space coverage. It samples the unit sphere around VOIs and uses an absorption-based reliability metric , solved via a branch-and-cutIP with an optimality gap as a quality measure. Empirical results compare against equidistant circular and greedy strategies, showing higher SSIM and PSNR and greater coverage (e.g., up to ~91% in some cases) with IP. The approach enables automated, data-complete trajectory design for complex objects and resource-constrained scans, with potential to reduce scan times and artifacts.

Abstract

X-ray computed tomography (CT) plays a key role in digitizing three-dimensional structures for a wide range of medical and industrial applications. Traditional CT systems often rely on standard circular and helical scan trajectories, which may not be optimal for challenging scenarios involving large objects, complex structures, or resource constraints. In response to these challenges, we are exploring the potential of twin robotic CT systems, which offer the flexibility to acquire projections from arbitrary views around the object of interest. Ensuring complete and mathematically sound reconstructions becomes critical in such systems. In this work, we present an integer programming-based CT trajectory optimization method. Utilizing discrete data completeness conditions, we formulate an optimization problem to select an optimized set of projections. This approach enforces data completeness and considers absorption-based metrics for reliability evaluation. We compare our method with an equidistant circular CT trajectory and a greedy approach. While greedy already performs well in some cases, we provide a way to improve greedy-based projection selection using an integer optimization approach. Our approach improves CT trajectories and quantifies the optimality of the solution in terms of an optimality gap.
Paper Structure (10 sections, 2 equations, 3 figures, 2 tables)

This paper contains 10 sections, 2 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Methods
  3. Continuous CT Data Completeness Condition
  4. Discrete CT Data Completeness Condition
  5. Integer Program for CT Trajectory Optimization
  6. Reference Methods
  7. Experiments and Results
  8. CT Trajectory Optimization for Metal Artifact Reduction
  9. CT Trajectory Optimization for an Arbitrary VOI
  10. Conclusion

Figures (3)

  • Figure 1: Optimized Projections for Test Specimen in Section \ref{['cube']}. Red projections represent the 25 selected ones, while blue indicates others.
  • Figure 2: Overview of the test specimen of Experiment \ref{['expA']}. (a) Sketch of the carbon test specimen. (b) Simulated projection of the test specimen, red box markes the projected VOI herl2022diss.
  • Figure 3: Optimized CT trajectory for the marked region. The optimized and circular CT trajectories consist of $k =25$ projections, while the reference data was a spherical CT trajectory with 1000 projections.