Remarks on the general funk transform and thermoacoustic tomography

Victor Palamodov

doi:10.3934/ipi.2010.4.693

Remarks on the general funk transform and thermoacoustic tomography

Victor Palamodov^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

24 Scopus citations

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.

Original language	English
Pages (from-to)	693-702
Number of pages	10
Journal	Inverse Problems and Imaging
Volume	4
Issue number	4
DOIs	https://doi.org/10.3934/ipi.2010.4.693
State	Published - Nov 2010

Keywords

Conjugate points
Elliptic PDO
Funk transform of a density
Kaczmarz method
Partial scan
Range conditions
Reciprocal Funk transform
Thermoacoustic tomography

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10.3934/ipi.2010.4.693

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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.",

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Remarks on the general funk transform and thermoacoustic tomography

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