Support curves of invertible Radon transforms
Let $S$ and the origin be different points of the closed curve $s$ in the plane. For any point $P$ there is exactly one orientation preserving similarity $A_P$ which fixes the origin and takes $S$ to $P$. The function transformation $$ _{s} f(P)=int_{A_{Ps}}f(X)d X$$ is said to be the Radon transfor...
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| Dokumentumtípus: | Cikk |
| Megjelent: |
1993
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| Sorozat: | ARCHIV DER MATHEMATIK
61 No. 5 |
| doi: | 10.1007/BF01207544 |
| mtmt: | 1118117 |
| Online Access: | http://publicatio.bibl.u-szeged.hu/15959 |
| Tartalmi kivonat: | Let $S$ and the origin be different points of the closed curve $s$ in the plane. For any point $P$ there is exactly one orientation preserving similarity $A_P$ which fixes the origin and takes $S$ to $P$. The function transformation $$ _{s} f(P)=int_{A_{Ps}}f(X)d X$$ is said to be the Radon transform with respect to the {it support curve} $s$, where $d X$ is the arclength measure on $A_{Ps}$. The invertibility of $ _{s}$ is proved on a subspace of the $ct$ functions if $s$ has strictly convex distance function. The support theorem is shown on a subspace of the $lt$ functions for curves having exactly two cross points with any of the circles centered to the origin. Counterexample shows the necessity of this condition. Finally a generalization to higher dimensions and a continuity result are given. |
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| Terjedelem/Fizikai jellemzők: | 448-458 |
| ISSN: | 0003-889X |