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

TL;DR

This paper investigates the injectivity of the circular Radon transform in thermoacoustic tomography, providing new insights using wave equation methods to understand when the transform uniquely determines a function.

Contribution

It offers new results on the injectivity of the circular Radon transform using wave equation techniques, expanding understanding in tomography and integral geometry.

Findings

New injectivity conditions established

Methods based on wave equation domain dependence

Enhanced understanding of transform's uniqueness properties

Abstract

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.