Handle URI:
http://hdl.handle.net/10754/599439
Title:
Range conditions for a spherical mean transform
Authors:
Agranovsky, Mark; Finch, David; Kuchment, Peter
Abstract:
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.
Citation:
Agranovsky M, Finch D, Kuchment P (2009) Range conditions for a spherical mean transform. IPI 3: 373–382. Available: http://dx.doi.org/10.3934/ipi.2009.3.373.
Publisher:
American Institute of Mathematical Sciences (AIMS)
Journal:
Inverse Problems and Imaging
KAUST Grant Number:
KUS-CI-016-04
Issue Date:
Jul-2009
DOI:
10.3934/ipi.2009.3.373
Type:
Article
ISSN:
1930-8337
Sponsors:
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.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorAgranovsky, Marken
dc.contributor.authorFinch, Daviden
dc.contributor.authorKuchment, Peteren
dc.date.accessioned2016-02-28T05:51:09Zen
dc.date.available2016-02-28T05:51:09Zen
dc.date.issued2009-07en
dc.identifier.citationAgranovsky M, Finch D, Kuchment P (2009) Range conditions for a spherical mean transform. IPI 3: 373–382. Available: http://dx.doi.org/10.3934/ipi.2009.3.373.en
dc.identifier.issn1930-8337en
dc.identifier.doi10.3934/ipi.2009.3.373en
dc.identifier.urihttp://hdl.handle.net/10754/599439en
dc.description.abstractThe 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.en
dc.description.sponsorshipThe 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.en
dc.publisherAmerican Institute of Mathematical Sciences (AIMS)en
dc.titleRange conditions for a spherical mean transformen
dc.typeArticleen
dc.identifier.journalInverse Problems and Imagingen
dc.contributor.institutionMathematics Department, Bar Ilan University, Ramat Gan 52900, Israelen
dc.contributor.institutionMathematics Department, Oregon State University, Corvallis, OR 97331-4605, United Statesen
dc.contributor.institutionMathematics Department, Texas A&M University, College Station, TX 77843-3368, United Statesen
kaust.grant.numberKUS-CI-016-04en
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