A Goal-Oriented Bayesian Experimental Design to Reduce Uncertainty in Sparse-Angle X-ray Computed Tomography
Abstract
Sparse-angle X-ray computed tomography (CT) presents a challenge for reliable inference, as limited measurements may leave object boundaries unresolved. Bayesian optimal experimental design (BOED) methods select informative measurements, but can be computationally expensive or require data-driven surrogates and do not explicitly exploit microlocal visibility. We address this limitation by focusing on estimating inclusion boundaries rather than the entire attenuation field. For piecewise-constant objects, these boundaries correspond to singularities characterized by their wavefront sets. Microlocal analysis determines the X-ray view-angles at which these singularities are visible. We combine this information with Bayesian uncertainty quantification to introduce B-MUSE, a microlocal uncertainty-driven sequential experimental design method. We define a microlocal C-optimality criterion associated with the wavefront direction of the most uncertain boundary singularity and prove that its optimal solution satisfies the microlocal visibility condition. B-MUSE uses this result to sequentially select informative view-angles according to boundary uncertainty. It also incorporates an adaptive stopping criterion that terminates acquisition when additional measurements provide no meaningful uncertainty reduction. We evaluate B-MUSE through numerical experiments, including interpretable examples, prior-generated inclusions, and a multi-inclusion example from an external dataset, and benchmark it against recent methods. The results show that B-MUSE substantially reduces posterior uncertainty with few adaptively selected measurements while providing boundary estimates. These findings establish a direct connection between BOED and microlocal visibility and demonstrate the potential of uncertainty-driven acquisition to reduce measurement requirements for goal-oriented X-ray CT without training data.
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BibTeX
@misc{sabour2026goaloriented,
title = {{A Goal-Oriented Bayesian Experimental Design to Reduce Uncertainty in Sparse-Angle X-ray Computed Tomography}},
author = {Mansoure Giahi Sabour and Hassan Yazdanian and Babak Maboudi Afkham},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.14528},
eprint = {2611.14528},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.14528},
}
RIS
TY - UNPB
TI - A Goal-Oriented Bayesian Experimental Design to Reduce Uncertainty in Sparse-Angle X-ray Computed Tomography
AU - Mansoure Giahi Sabour
AU - Hassan Yazdanian
AU - Babak Maboudi Afkham
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.14528
UR - https://arxiv.org/abs/2611.14528
AB - Sparse-angle X-ray computed tomography (CT) presents a challenge for reliable inference, as limited measurements may leave object boundaries unresolved. Bayesian optimal experimental design (BOED) methods select informative measurements, but can be computationally expensive or require data-driven surrogates and do not explicitly exploit microlocal visibility. We address this limitation by focusing on estimating inclusion boundaries rather than the entire attenuation field. For piecewise-constant objects, these boundaries correspond to singularities characterized by their wavefront sets. Microlocal analysis determines the X-ray view-angles at which these singularities are visible. We combine this information with Bayesian uncertainty quantification to introduce B-MUSE, a microlocal uncertainty-driven sequential experimental design method. We define a microlocal C-optimality criterion associated with the wavefront direction of the most uncertain boundary singularity and prove that its optimal solution satisfies the microlocal visibility condition. B-MUSE uses this result to sequentially select informative view-angles according to boundary uncertainty. It also incorporates an adaptive stopping criterion that terminates acquisition when additional measurements provide no meaningful uncertainty reduction. We evaluate B-MUSE through numerical experiments, including interpretable examples, prior-generated inclusions, and a multi-inclusion example from an external dataset, and benchmark it against recent methods. The results show that B-MUSE substantially reduces posterior uncertainty with few adaptively selected measurements while providing boundary estimates. These findings establish a direct connection between BOED and microlocal visibility and demonstrate the potential of uncertainty-driven acquisition to reduce measurement requirements for goal-oriented X-ray CT without training data.
ER -