An identity for triplets of double Hilbert transforms, with applications to the attenuated Radon transform
2012 (English)In: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 28, no 12, 125007- p.Article in journal (Refereed) Published
We consider an elementary identity for double singular integrals in the plane and show that one can apply this to deduce inversion and product formulae for the Hilbert transform and inversion formulae for the affine and weighted Radon transforms. We will be able to allow many of the previously known weights for which there is an inversion formula for the weighted Radon transform and also pose some new conditions on which weights that can be used.
Place, publisher, year, edition, pages
2012. Vol. 28, no 12, 125007- p.
IdentifiersURN: urn:nbn:se:kth:diva-109617DOI: 10.1088/0266-5611/28/12/125007ISI: 000312103100008ScopusID: 2-s2.0-84870466873OAI: oai:DiVA.org:kth-109617DiVA: diva2:583471
FunderKnut and Alice Wallenberg Foundation, KAW 2005.0098
QC 201301082013-01-082013-01-082014-02-28Bibliographically approved