RANGE CONDITIONS FOR A SPHERICAL MEAN TRANSFORM Academic Article

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.

authors

• Kuchment, Peter

published proceedings

• INVERSE PROBLEMS AND IMAGING

author list (cited authors)

• Agranovsky, M., Finch, D., & Kuchment, P.

citation count

• 26

complete list of authors

• Agranovsky, Mark||Finch, David||Kuchment, Peter

publication date

• February 2009

publisher

• American Institute of Mathematical Sciences (AIMS)  Publisher

published in

• Inverse Problems and Imaging  Journal

keywords

• Radon Transform
• Range
• Spherical Mean
• Tomography

Digital Object Identifier (DOI)

• 10.3934/ipi.2009.3.373

start page

• 373

end page

• 382

volume

• 3

issue

• 3

URL

• http://dx.doi.org/10.3934/ipi.2009.3.373