3D Image Reconstruction from X-Ray Measurements with Overlap

TL;DR

This paper introduces a novel 3D image reconstruction model that handles overlapping X-ray measurements using nonlinear constraints, enabling improved imaging in advanced X-ray scanner designs.

Contribution

It develops a new nonlinear constrained reconstruction model for overlapping X-ray data and proposes an algorithm to solve the resulting optimization problem.

Findings

Enhanced image quality in simulated measurements

Successful application to real-world data

Partially convex optimization problem solved effectively

Abstract

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.