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Stability estimates for the local Radon transform
Stockholm University, Faculty of Science, Department of Mathematics.ORCID iD: 0000-0002-0766-7049
Stockholm University, Faculty of Science, Department of Mathematics.ORCID iD: 0000-0003-1885-6387
2018 (English)In: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 34, no 3, article id 034004Article in journal (Refereed) Published
Abstract [en]

We consider the inverse problem for the 2-dimensional local Radon transform R[f], where f is supported in y >= x(2) and R[f](xi, eta) = integral f (x, xi x + eta) dx is defined near (xi, eta) = (0, 0). We give logarithmic estimates of f in terms of R[f] for functions f that satisfy an a priori bound. For a certain class of smooth, positive weight functions m we give similar estimates for the weighted Radon transform R-m vertical bar f](xi, eta) = integral f (x, xi x + eta) m(xi, eta, x) dx.

Place, publisher, year, edition, pages
2018. Vol. 34, no 3, article id 034004
Keywords [en]
radon transform, local injectivity, stability estimates
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-152161DOI: 10.1088/1361-6420/aaa99cISI: 000424903700001OAI: oai:DiVA.org:su-152161DiVA, id: diva2:1177908
Available from: 2018-01-26 Created: 2018-01-26 Last updated: 2018-03-06Bibliographically approved

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