by Joonas Ilmavirta, Keijo Mönkkönen, Jesse Railo
Abstract:
The geodesic ray transform, the mixed ray transform and the transverse ray transform of a tensor field on a surface can all be seen as what we call mixing ray transforms, compositions of the geodesic ray transform and an invertible linear map on tensor fields. We provide an approach that uses a unifying concept of symmetry to merge various earlier transforms (including mixed, transverse, and light ray transforms) into a single family of integral transforms with similar kernels.
Reference:
On mixed and transverse ray transforms on orientable surfaces (Joonas Ilmavirta, Keijo Mönkkönen, Jesse Railo), Journal of Inverse and Ill-Posed Problems, volume 31, number 1, pp. 43–63, 2023.
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The geodesic ray transform, the mixed ray transform and the transverse ray transform of a tensor field on a surface can all be seen as what we call mixing ray transforms, compositions of the geodesic ray transform and an invertible linear map on tensor fields. We provide an approach that uses a unifying concept of symmetry to merge various earlier transforms (including mixed, transverse, and light ray transforms) into a single family of integral transforms with similar kernels.
[arXiv]
Bibtex Entry:
@article{mixing-ray-transform,
author = {Joonas Ilmavirta and Keijo M{\"o}nkk{\"o}nen and Jesse Railo},
title = {{On mixed and transverse ray transforms on orientable surfaces}},
journal = {Journal of Inverse and Ill-Posed Problems},
month = jan,
year = {2023},
arxiv = {2009.01043},
url={http://users.jyu.fi/~jojapeil/pub/mixing-ray-transform.pdf},
gsid = {14864668223247799264},
abstract = {The geodesic ray transform, the mixed ray transform and the transverse ray transform of a tensor field on a surface can all be seen as what we call mixing ray transforms, compositions of the geodesic ray transform and an invertible linear map on tensor fields. We provide an approach that uses a unifying concept of symmetry to merge various earlier transforms (including mixed, transverse, and light ray transforms) into a single family of integral transforms with similar kernels.},
volume = 31,
number = 1,
pages = {43--63},
doi = {10.1515/jiip-2022-0009}
}