Inverse Problems and Imaging (IPI)

Remarks on the general Funk transform and thermoacoustic tomography

Pages: 693 - 702, Volume 4, Issue 4, November 2010      doi:10.3934/ipi.2010.4.693

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Victor Palamodov - School of Mathematical Sciences, Tel Aviv University, Ramat Aviv Tel Aviv 69978, Israel (email)

Abstract: We discuss properties of a generalized Minkowski-Funk transform defined for a family of hypersurfaces. We prove two-side estimates and show that the range conditions can be written in terms of the reciprocal Funk transform. Some applications to the spherical mean transform are considered.

Keywords:  Funk transform of a density, conjugate points, reciprocal Funk transform, elliptic PDO, range conditions, thermoacoustic tomography, partial scan, Kaczmarz method.
Mathematics Subject Classification:  Primary: 53C65; Secondary: 65R32, 78A46.

Received: June 2009;      Available Online: September 2010.