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Novikov's inversion formula for the attenuated radon transform - A new approach
KTH, Superseded Departments, Mathematics.
2004 (English)In: Journal of Geometric Analysis, ISSN 1050-6926, E-ISSN 1559-002X, Vol. 14, no 2, 185-198 p.Article in journal (Refereed) Published
Abstract [en]

We study the inversion of weighted Radon transforms in two dimensions, R-rho f (L) = f(L) f((.)) rho (L, (.)) ds, where the weight function rho (L, x), L a line and x is an element of L, has a special form. It was an important breakthrough when R. G. Novikov recently gave an explicit formula for the inverse of R-rho When rho has the form (1.2); in this case R-rho is called the attenuated Radon transform. Here. we prove similar results,for a somewhat larger class of rho using completely different and quite elementary methods.

Place, publisher, year, edition, pages
2004. Vol. 14, no 2, 185-198 p.
Keyword [en]
attenuated Radon transform, generalized Radon transform, weighted Radon transform
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-23661DOI: 10.1007/BF02922067ISI: 000223406900001Scopus ID: 2-s2.0-84867961903OAI: oai:DiVA.org:kth-23661DiVA: diva2:342360
Note
QC 20100525 QC 20111101Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2017-12-12Bibliographically approved

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