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PreprintCC BY 4.0arXiv

Non-integral geometry: additional term fA as a regularizing term

  • I. V. Anikin
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Abstract

In the present paper, we first describe the principal basis of non-integral geometry. Non-integral geometry is a new field of generalized function (distribution) theory where the effects breaking the symmetry of integration measure have been investigated. In turn, the non-symmetric integration measure (the non-invariant measure) leads to the complex form of the universal, dimension-independent inverse operator with the additional contributions compared to the methods of integral geometry. The additional term with the complex integration measure serves to the extension that improves the image reconstruction procedure. Then, we prove that this additional term fA in the universal inverse Radon transforms plays a role of the regularizing contribution. In particular, we show that owing to the presence of fA the corresponding complex singularities can be eliminated in the image reconstruction process.

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Cite

BibTeXRIS
BibTeX
@misc{anikin2026nonintegral,
  title = {{Non-integral geometry: additional term $f_A$ as a regularizing term}},
  author = {I. V. Anikin},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.28670},
  eprint = {2605.28670},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.28670},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Non-integral geometry: additional term f_A as a regularizing term
AU  - I. V. Anikin
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2605.28670
UR  - https://arxiv.org/abs/2605.28670
AB  - In the present paper, we first describe the principal basis of non-integral geometry. Non-integral geometry is a new field of generalized function (distribution) theory where the effects breaking the symmetry of integration measure have been investigated. In turn, the non-symmetric integration measure (the non-invariant measure) leads to the complex form of the universal, dimension-independent inverse operator with the additional contributions compared to the methods of integral geometry. The additional term with the complex integration measure serves to the extension that improves the image reconstruction procedure. Then, we prove that this additional term f_A in the universal inverse Radon transforms plays a role of the regularizing contribution. In particular, we show that owing to the presence of f_A the corresponding complex singularities can be eliminated in the image reconstruction process.
ER  -