Integer Optimization of CT Trajectories using a Discrete Data Completeness Formulation
This work addresses the need for more efficient and reliable CT imaging in medical and industrial applications, offering an incremental improvement over existing methods for projection selection.
The paper tackles the problem of optimizing CT scan trajectories for twin robotic systems by formulating an integer programming method based on discrete data completeness conditions, resulting in improved trajectories with quantified optimality gaps compared to equidistant circular and greedy approaches.
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.