A Method for Gamma-Ray Energy Spectrum Inversion and Correction

Accurate spectral analysis of high-energy astrophysical sources often relies on comparing observed data to incident spectral models convolved with the instrument response. However, for Gamma-Ray Bursts and other high-energy transient events observed at high count rates, significant distortions (e.g., pile-up, dead time, and large signal trailing) are introduced, complicating this analysis. We present a method framework to address the model dependence problem, especially to solve the problem of energy spectrum distortion caused by instrument signal pile-up due to high counting rate and high-rate effects, applicable to X-ray, gamma-ray, and particle detectors. Our approach combines physics-based Monte Carlo (MC) simulations with a model-independent spectral inversion technique. The MC simulations quantify instrumental effects and enable correction of the distorted spectrum. Subsequently, the inversion step reconstructs the incident spectrum using an inverse response matrix approach, conceptually equivalent to deconvolving the detector response. The inversion employs a Convolutional Neural Network, selected for its numerical stability and effective handling of complex detector responses. Validation using simulations across diverse input spectra demonstrates high fidelity. Specifically, for 27 different parameter sets of the brightest gamma-ray bursts, goodness-of-fit tests confirm the reconstructed spectra are in excellent statistical agreement with the input spectra, and residuals are typically within $\pm 2\sigma$. This method enables precise analysis of intense transients and other high-flux events, overcoming limitations imposed by instrumental effects in traditional analyses.