Bayesian Image Reconstruction with Spatially Variant PSFs in X-ray Astronomy
Abstract
X-ray observatories introduce unwanted instrumental effects into photon count data that must be accurately accounted for. In particular, the spatially variant point spread function (PSF) and shot noise pose a non-trivial inverse problem. We apply Bayesian inference grounded in information field theory (IFT) combined with a fast spatially variant PSF representation to infer the posterior mean and uncertainty of the X-ray flux under a minimal set of physically motivated prior assumptions, thereby removing or reducing these instrumental effects. First, ignoring spatial PSF variability, the IFT-based deconvolution is benchmarked on a synthetic example against three variants of the Richardson-Lucy (RL) algorithm using SSIM, RMSE, and NLL as evaluation metrics. Second, the ability of an interpolated patch-based convolution scheme to accurately represent the complex, spatially variant Chandra PSF is assessed on simulated PSF data. Finally, deblurring and spatially variant PSF representation are combined and applied to real Chandra observations of the supernova remnant Cassiopeia A. The IFT-based deconvolution outperforms all tested RL variants on the synthetic benchmark. The patch-based convolution scheme accurately recovers the complex structure of the Chandra PSF. Applied to Cassiopeia A, the reconstructed image appears visually sharper than the exposure-corrected data, and the data residuals are consistent with pure noise, indicating an accurate model of both the instrument and the sky. A comparison with a highly resolved reference dataset confirms this impression. The presented framework enables the removal of spatially variant PSFs from noisy data and opens avenues for future work on cross-calibration between multiple observations or different X-ray instruments, building on the principled uncertainty quantification inherent to the Bayesian framework.
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BibTeX
@misc{eberle2026bayesian,
title = {{Bayesian Image Reconstruction with Spatially Variant PSFs in X-ray Astronomy}},
author = {Vincent Eberle and Matteo Guardiani and Margret Westerkamp and Philipp Arras and Philipp Frank and Julia Stadler and Torsten Enßlin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02062},
eprint = {2610.02062},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02062},
}
RIS
TY - UNPB
TI - Bayesian Image Reconstruction with Spatially Variant PSFs in X-ray Astronomy
AU - Vincent Eberle
AU - Matteo Guardiani
AU - Margret Westerkamp
AU - Philipp Arras
AU - Philipp Frank
AU - Julia Stadler
AU - Torsten Enßlin
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.02062
UR - https://arxiv.org/abs/2610.02062
AB - X-ray observatories introduce unwanted instrumental effects into photon count data that must be accurately accounted for. In particular, the spatially variant point spread function (PSF) and shot noise pose a non-trivial inverse problem. We apply Bayesian inference grounded in information field theory (IFT) combined with a fast spatially variant PSF representation to infer the posterior mean and uncertainty of the X-ray flux under a minimal set of physically motivated prior assumptions, thereby removing or reducing these instrumental effects. First, ignoring spatial PSF variability, the IFT-based deconvolution is benchmarked on a synthetic example against three variants of the Richardson-Lucy (RL) algorithm using SSIM, RMSE, and NLL as evaluation metrics. Second, the ability of an interpolated patch-based convolution scheme to accurately represent the complex, spatially variant Chandra PSF is assessed on simulated PSF data. Finally, deblurring and spatially variant PSF representation are combined and applied to real Chandra observations of the supernova remnant Cassiopeia A. The IFT-based deconvolution outperforms all tested RL variants on the synthetic benchmark. The patch-based convolution scheme accurately recovers the complex structure of the Chandra PSF. Applied to Cassiopeia A, the reconstructed image appears visually sharper than the exposure-corrected data, and the data residuals are consistent with pure noise, indicating an accurate model of both the instrument and the sky. A comparison with a highly resolved reference dataset confirms this impression. The presented framework enables the removal of spatially variant PSFs from noisy data and opens avenues for future work on cross-calibration between multiple observations or different X-ray instruments, building on the principled uncertainty quantification inherent to the Bayesian framework.
ER -