Non-integral geometry: additional term $f_A$ as a regularizing term
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913168325869568 |
|---|---|
| author | Anikin, I. V. |
| author_facet | Anikin, I. V. |
| contents | 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 proof 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_28670 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-integral geometry: additional term $f_A$ as a regularizing term Anikin, I. V. High Energy Physics - Theory Mathematical Physics Functional Analysis 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 proof 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. |
| title | Non-integral geometry: additional term $f_A$ as a regularizing term |
| topic | High Energy Physics - Theory Mathematical Physics Functional Analysis |
| url | https://arxiv.org/abs/2605.28670 |