A range description for the planar circular Radon transform

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dc.creatorAmbartsoumian, Gaik
dc.creatorKuchment, Peter
dc.date2005-08-04
dc.date.accessioned2026-07-07T06:30:44Z
dc.date.available2026-07-07T06:30:44Z
dc.descriptionThe transform considered in the paper integrates a function supported in the unit disk on the plane over all circles centered at the boundary of this disk. Such circular Radon transform arises in several contemporary imaging techniques, as well as in other applications. As it is common for transforms of Radon type, its range has infinite co-dimension in standard function spaces. Range descriptions for such transforms are known to be very important for computed tomography, for instance when dealing with incomplete data, error correction, and other issues. A complete range description for the circular Radon transform is obtained. Range conditions include the recently found set of moment type conditions, which happens to be incomplete, as well as the rest of conditions that have less standard form. In order to explain the procedure better, a similar (non-standard) treatment of the range conditions is described first for the usual Radon transform on the plane.
dc.descriptionsubmitted for publication
dc.identifierhttps://arxiv.org/abs/math/0508082
dc.identifierhttp://arxiv.org/abs/math/0508082
dc.identifierSIAM J. Math. Anal. vol. 38, no. 2, 2006, 681-692
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/98413
dc.subjectGeneral Mathematics
dc.subjectMathematical Physics
dc.subject44A12, 65R10, 65R32, 92C55
dc.titleA range description for the planar circular Radon transform
dc.typetext

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