A Data-driven Approach to X-Ray Spectral Fitting: Quasi-deconvolution

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.