  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.
