High-energy X-ray spectrum reconstruction: solving the inverse problem from optimized multi-material transmission measurements

TL;DR

This paper advances high-energy X-ray spectrum reconstruction by optimizing multi-material transmission measurements, significantly reducing system matrix condition numbers, and introducing a noise-robust reconstruction method suitable for challenging high-energy sources.

Contribution

It generalizes the measurement optimization approach to multiple calibration materials and develops a noise-robust reconstruction method for high-energy X-ray spectra.

Findings

Optimized calibration materials significantly lower the system matrix condition number.

The proposed method achieves realistic noise levels in simulations with scatter noise.

The noise-robust reconstruction method outperforms traditional expectation-maximization approaches.

Abstract

Reconstructing the unknown spectrum of a given X-ray source is a common problem in a wide range of X-ray imaging tasks. For high-energy sources, transmission measurements are mostly used to recover the X-ray spectrum, as a solution to an inverse problem. While this inverse problem is usually under-determined, ill-posedness can be reduced by improving the choice of transmission measurements. A recently proposed approach optimizes custom thicknesses of calibration materials used to generate transmission measurements, employing a genetic algorithm to minimize the condition number of the system matrix before inversion. In this paper, we generalize the proposed approach to multiple calibration materials and show a much larger decrease of the condition number of the system matrix than thickness-only optimization. Additionally, the spectrum reconstruction pipeline is tested in a simulation study with a challenging high-energy Bremsstrahlung X-ray source encountered in Linear Induction Accelerators (LIA), with strong scatter noise. Using this approach, a realistic noise level is obtained on measurements. A generic anti-scatter grid is designed to reduce noise to an acceptable -- yet still high -- noise range. A novel noise-robust reconstruction method is then presented, which shows much less sensitive to initialization than common expectation-maximization approaches, enables a precise choice of spectrum resolution and a controlled injection of prior knowledge of the X-ray spectrum.