  X-ray spectral fitting of astronomical sources requires convolving the
intrinsic spectrum or model with the instrumental response. Standard forward
modeling techniques have proven success in recovering the underlying physical
parameters in moderate to high signal-to-noise regimes; however, they struggle
to achieve the same level of accuracy in low signal-to-noise regimes.
Additionally, the use of machine learning techniques on X-ray spectra requires
access to the intrinsic spectrum. Therefore, the measured spectrum must be
effectively deconvolved from the instrumental response. In this note, we
explore numerical methods for inverting the matrix equation describing X-ray
spectral convolution. We demonstrate that traditional methods are insufficient
to recover the intrinsic X-ray spectrum and argue that a novel approach is
required.
