Integer Optimization of CT Trajectories using a Discrete Data
  Completeness Formulation
Linda-Sophie Schneider Gabriel Herl Andreas Maier
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.