Range conditions for a spherical mean transform

Details Range conditions for a spherical mean transform Range conditions for a spherical mean transform

2009-02-25

arxiv.org/abs/0902.4272v3

Inverse Problems and Imaging, Volume 3, No. 3, 2009, 373-382

Mathematics

Analysis of PDEs

Scientific paper

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.

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