Uncertainty quantification of Abel inversion in multi-energy x-ray radiography with spatially varying noise

Abel inversion is a classical technique for reconstructing the volumetric density of axisymmetric objects from line-integral projections in x-ray radiography. However, traditional methods often rely on simplifying assumptions such as monochromatic x-ray sources and homoscedastic Gaussian noise, which do not hold in practical experiments such as micron-ejecta studies. This paper presents a hierarchical Bayesian framework with Markov Chain Monte Carlo sampling for uncertainty quantification in Abel inversion under more realistic conditions, including polychromatic x-ray spectra and spatially varying noise. We introduce a “step wedge method” to calibrate the energy spectrum and noise characteristics and propose a modified prior structure to improve reconstruction accuracy near the symmetry axis. The method is validated on both synthetic and real experimental data from a 4 MeV pulsed x-ray radiography system. Results demonstrate accurate density reconstruction with explicit uncertainty bounds, highlighting the method’s robustness and applicability in dynamic imaging diagnostics.