On the injectivity of the circular Radon transform arising in thermoacoustic tomography

Details On the injectivity of the circular Radon transform arising in thermoacoustic tomography On the injectivity of the circular Radon transform arising in thermoacoustic tomography

2004-04-27

arxiv.org/abs/math-ph/0404065v3

Inverse Problems 21 (2005), 473-485

Physics

Mathematical Physics

To appear in Inverse Problems

Scientific paper

10.1088/0266-5611/21/2/004

The circular Radon transform integrates a function over the set of all spheres with a given set of centers. The problem of injectivity of this transform (as well as inversion formulas, range descriptions, etc.) arises in many fields from approximation theory to integral geometry, to inverse problems for PDEs, and recently to newly developing types of tomography. The article discusses known and provides new results that one can obtain by methods that essentially involve only the finite speed of propagation and domain dependence for the wave equation.

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