  The photon flux resulting from high-energy electron beam interactions with
high field systems, such as in the upcoming FACET-II experiments at SLAC
National Accelerator Laboratory, may give deep insight into the electron beam's
underlying dynamics at the interaction point. Extraction of this information is
an intricate process, however. To demonstrate how to approach this challenge
with modern methods, this paper utilizes data from simulated plasma wakefield
acceleration-derived betatron radiation experiments and high-field
laser-electron-based radiation production to determine reliable methods of
reconstructing key beam and interaction properties. For these measurements,
recovering the emitted 200 keV to 10 GeV photon energy spectra from two
advanced spectrometers now being commissioned requires testing multiple methods
to finalize a pipeline from their responses to incident electron beam
information. In each case, we compare the performance of: neural networks,
which detect patterns between data sets through repeated training; maximum
likelihood estimation (MLE), a statistical technique used to determine unknown
parameters from the distribution of observed data; and a hybrid approach
combining the two. Further, in the case of photons with energies above 30 MeV,
we also examine the efficacy of QR decomposition, a matrix decomposition
method. The betatron radiation and the high-energy photon cases demonstrate the
effectiveness of a hybrid ML-MLE approach, while the high-field electrodynamics
interaction and the low-energy photon cases showcased the machine learning (ML)
model's efficiency in the presence of noise. As such, while there is utility in
all the methods, the ML-MLE hybrid approach proves to be the most
generalizable.
