  3D image reconstruction from a set of X-ray projections is an important image
reconstruction problem, with applications in medical imaging, industrial
inspection and airport security. The innovation of X-ray emitter arrays allows
for a novel type of X-ray scanners with multiple simultaneously emitting
sources. However, two or more sources emitting at the same time can yield
measurements from overlapping rays, imposing a new type of image reconstruction
problem based on nonlinear constraints. Using traditional linear reconstruction
methods, respective scanner geometries have to be implemented such that no rays
overlap, which severely restricts the scanner design. We derive a new type of
3D image reconstruction model with nonlinear constraints, based on measurements
with overlapping X-rays. Further, we show that the arising optimization problem
is partially convex, and present an algorithm to solve it. Experiments show
highly improved image reconstruction results from both simulated and real-world
measurements.
