Lionheart, William R.B.
(2018)
*Notes on Histotomography.*
[MIMS Preprint]

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## Abstract

In many tomographic imaging problems the data consists of integrals along lines or curves. Increas- ingly we are seeing “rich tomography” problems where the quantity imaged is higher dimensional than a scalar per voxel, including vectors tensors and functions. The data can also be higher dimensional and in many cases consists of a one or two dimensional spectrum for each ray. In many such cases the data contains not just integrals along rays but the distribution of values along the ray. If this is discretized into bins we can think of this as a histogram. In this talk we introduce the concept of “histotomogra- phy”. For scalar problems with histogram data this holds the possibility of reconstruction with fewer rays. In vector and tensor problems it holds the promise of reconstruction of images that are in the null space of related integral transforms. We will illustrate with examples from scalar spectral attenuation tomography and tensor tomography methods for strain using neutrons, electrons and x-rays.

Item Type: | MIMS Preprint |
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Uncontrolled Keywords: | histotomography, spectral tomography, chemical species tomography, doppler tomography, Bragg edge strain tomography, electron strain tomography |

Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 45 Integral equations MSC 2010, the AMS's Mathematics Subject Classification > 53 Differential geometry |

Depositing User: | Prof WRB Lionheart |

Date Deposited: | 09 Mar 2018 05:22 |

Last Modified: | 09 Mar 2018 05:22 |

URI: | https://eprints.maths.manchester.ac.uk/id/eprint/2627 |

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