Invertible Low-Dimensional Modelling of X-ray Absorption Spectra for Potential Applications in Spectral X-ray Imaging

TL;DR

This paper introduces a novel invertible low-dimensional model combining neural networks and linear algebra to efficiently model and invert X-ray absorption spectra, especially those with K-edges, for improved spectral X-ray imaging applications.

Contribution

A new non-linear model integrating a deep autoencoder with SVD for better inversion of X-ray spectra including K-edges, surpassing existing models in accuracy and utility.

Findings

Outperforms traditional models in spectral accuracy.

Effective for spectra with K-edges.

Enables efficient model inversion for spectral imaging.

Abstract

X-ray interaction with matter is an energy-dependent process that is contingent on the atomic structure of the constituent material elements. The most advanced models to capture this relationship currently rely on Monte Carlo (MC) simulations. Whilst these very accurate models, in many problems in spectral X-ray imaging, such as data compression, noise removal, spectral estimation, and the quantitative measurement of material compositions, these models are of limited use, as these applications typically require the efficient inversion of the model, that is, they require the estimation of the best model parameters for a given spectral measurement. Current models that can be easily inverted however typically only work when modelling spectra in regions away from their K-edges, so they have limited utility when modelling a wider range of materials. In this paper, we thus propose a novel, non-linear model that combines a deep neural network autoencoder with an optimal linear model based on the Singular Value Decomposition (SVD). We compare our new method to other alternative linear and non-linear approaches, a sparse model and an alternative deep learning model. We demonstrate the advantages of our method over traditional models, especially when modelling X-ray absorption spectra that contain K-edges in the energy range of interest.