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Stability of the inverse problem for the attenuated Radon transform with 180 degrees data
Stockholm University, Faculty of Science, Department of Mathematics. Matematik.
2004 (English)In: Inverse Problems, Vol. 20, no 3, 781-797 p.Article in journal (Refereed) Published
Abstract [en]

We consider the inverse problem for the attenuated Radon transform in two dimensions. It has recently been shown that this problem has a unique solution when the attenuation function is Hölder continuous, even with limited angle data. In this paper, we study stability of the inverse problem, with data from a 180° range of angles. We show that when the attenuation function is Hölder continuous and the support of the original function f is restricted to a given compact set, the Hölder norm of f with exponent -1/2 can be estimated in terms of the L2 norm of the attenuated Radon transform of f. We also obtain new stability results for the forward problem, that is, estimates of the norm of the Radon transform in terms of norms of the original function and the attenuation function.

Place, publisher, year, edition, pages
2004. Vol. 20, no 3, 781-797 p.
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:su:diva-20257DOI: doi:10.1088/0266-5611/20/3/008OAI: oai:DiVA.org:su-20257DiVA: diva2:186783
Available from: 2007-11-23 Created: 2007-11-23 Last updated: 2011-01-12Bibliographically approved

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Publisher's full texthttp://www.iop.org/EJ/abstract/0266-5611/20/3/008

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