Stability of the non-abelian \(X\)-ray transform in dimension \(\ge 3\)

DOI10.1007/s12220-021-00679-0zbMath1486.53087arXiv2008.07951OpenAlexW3160689279MaRDI QIDQ2238550

Jan Bohr

Publication date: 1 November 2021

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.07951

zbMATH Keywords

inverse problemsmicrolocal analysisanalysis of PDE'snon-abelian X-ray tomography

Mathematics Subject Classification ID

Integral geometry (53C65) Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs (35A27) Numerical methods for inverse problems for integral equations (65R32)

Related Items (2)

Stability estimate for the broken non-abelian x-ray transform in Minkowski space ⋮ Convergence Rates for Learning Linear Operators from Noisy Data

Cites Work

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• Integral geometry for tensor fields. Transl. from the Russian
• The attenuated ray transform for connections and Higgs fields
• Local and global boundary rigidity and the geodesic X-ray transform in the normal gauge
• The inverse problem for the local geodesic ray transform
• Boundary rigidity with partial data
• Local non-injectivity for weighted radon transforms
• Mathematical Foundations of Infinite-Dimensional Statistical Models
• ON DETERMINATION OF A GAUGE FIELD ON ℝ^d FROM ITS NON-ABELIAN RADON TRANSFORM ALONG ORIENTED STRAIGHT LINES
• Consistent Inversion of Noisy <scp>Non‐Abelian X‐Ray</scp> Transforms
• Consistency of Bayesian inference with Gaussian process priors in an elliptic inverse problem
• The geodesic X-ray transform with matrix weights
• Royen’s Proof of the Gaussian Correlation Inequality
• Fundamentals of Nonparametric Bayesian Inference

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