Efficient nonparametric Bayesian inference for $X$-ray transforms

@article{Monard2017EfficientNB,
  title={Efficient nonparametric Bayesian inference for \$X\$-ray transforms},
  author={Franccois Monard and Richard Nickl and Gabriel P. Paternain},
  journal={The Annals of Statistics},
  year={2017}
}
We consider the statistical inverse problem of recovering a function $f: M \to \mathbb R$, where $M$ is a smooth compact Riemannian manifold with boundary, from measurements of general $X$-ray transforms $I_a(f)$ of $f$, corrupted by additive Gaussian noise. For $M$ equal to the unit disk with `flat' geometry and $a=0$ this reduces to the standard Radon transform, but our general setting allows for anisotropic media $M$ and can further model local `attenuation' effects -- both highly relevant… 

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