TY - JOUR
T1 - Range conditions for a spherical mean transform
AU - Agranovsky, Mark
AU - Finch, David
AU - Kuchment, Peter
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-CI-016-04
Acknowledgements: The work of the first author was partially supported by the ISF (Israel Science Foundation) Grant 688/08 and by the Texas A&M University. The third author was partially supported by the NSF grant DMS 0604778 and by the KAUST grant KUS-CI-016-04. The authors express their gratitude to NSF, Texas A&M University, and KAUST for the support. The authors also thank Y. Lyubarskii and L. Nguyen for discussions and the referee for useful remarks.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
PY - 2009/7/31
Y1 - 2009/7/31
N2 - The paper is devoted to the range description of the Radon type transform that averages a function over all spheres centered on a given sphere. Such transforms arise naturally in thermoacoustic tomography, a novel method of medical imaging. Range descriptions have recently been obtained for such transforms, and consisted of smoothness and support conditions, moment conditions, and some additional orthogonality conditions of spectral nature. It has been noticed that in odd dimensions, surprisingly, the moment conditions are superfluous and can be eliminated. It is shown in this text that in fact the same happens in any dimension.
AB - The paper is devoted to the range description of the Radon type transform that averages a function over all spheres centered on a given sphere. Such transforms arise naturally in thermoacoustic tomography, a novel method of medical imaging. Range descriptions have recently been obtained for such transforms, and consisted of smoothness and support conditions, moment conditions, and some additional orthogonality conditions of spectral nature. It has been noticed that in odd dimensions, surprisingly, the moment conditions are superfluous and can be eliminated. It is shown in this text that in fact the same happens in any dimension.
UR - http://hdl.handle.net/10754/599439
UR - http://aimsciences.org//article/doi/10.3934/ipi.2009.3.373
U2 - 10.3934/ipi.2009.3.373
DO - 10.3934/ipi.2009.3.373
M3 - Article
SN - 1930-8337
VL - 3
SP - 373
EP - 382
JO - Inverse Problems and Imaging
JF - Inverse Problems and Imaging
IS - 3
ER -