Abstract
Considerations of the non-Abelian Radon transform were started in [Man-akov, Zakharov, 1981] in the framework of the theory of solitons in dimension 2 +1. On the other hand, the problem of inversion of transforms of such a type arises in different tomographies, including emission tomographies, polarization tomographies, and vector field tomography. In this article, we give a short review of old and recent results on this subject. This article is an extended version of the talk given at the conference "100 Years of the Radon Transform, " Linz, 27-31 March 2017.
| Original language | English |
|---|---|
| Title of host publication | The Radon Transform |
| Subtitle of host publication | The First 100 Years and Beyond |
| Publisher | De Gruyter |
| Pages | 115-127 |
| Number of pages | 13 |
| ISBN (Electronic) | 9783110560855 |
| ISBN (Print) | 9783110559415 |
| DOIs | |
| Publication status | Published - 17 Jun 2019 |
| Externally published | Yes |
Keywords
- Integral geometry
- Inverse connection problem
- Inverse scattering
- Non-Abelian Radon transform
- Theory of solitons
- Tomography
- Yang-Mills fields
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