Remarks on the general Funk transform and thermoacoustic tomography
Victor Palamodov
Inverse Problems & Imaging 2010, 4(4): 693-702 doi: 10.3934/ipi.2010.4.693
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: Kaczmarz method. elliptic PDO Funk transform of a density reciprocal Funk transform partial scan conjugate points thermoacoustic tomography range conditions

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