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LOCAL SOBOLEV ESTIMATES OF A FUNCTION BY MEANS OF ITS RADON TRANSFORM
Stockholm University, Faculty of Science, Department of Mathematics.
2010 (English)In: Inverse Problems and Imaging, ISSN 1930-8337, Vol. 4, no 4, 721-734 p.Article in journal (Refereed) Published
Abstract [en]

In this article, we will define local and microlocal Sobolev seminorms and prove local and microlocal inverse continuity estimates for the Radon hyperplane transform in these seminorms. The relation between the Sobolev wavefront set of a function f and of its Radon transform is well-known [18]. However, Sobolev wavefront is qualitative and therefore the relation in [18] is qualitative. Our results will make the relation between singularities of a function and those of its Radon transform quantitative. This could be important for practical applications, such as tomography, in which the data are smooth but can have large derivatives.

Place, publisher, year, edition, pages
2010. Vol. 4, no 4, 721-734 p.
Keyword [en]
Radon transform, limited data tomography, Sobolev seminorms, wavefront set, singularity detection
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-66222DOI: 10.3934/ipi.2010.4.721ISI: 000282648200016OAI: oai:DiVA.org:su-66222DiVA: diva2:467685
Note
authorCount :2Available from: 2011-12-19 Created: 2011-12-19 Last updated: 2011-12-19Bibliographically approved

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