Inversion Formula for a Radon-Type Transform Arising in Photoacoustic Tomography with Circular Integrating Detectors

Exact Series Reconstruction in Photoacoustic Tomography with Circular Integrating Detectors

A method for photoacoustic tomography is presented that uses circular integrals of the acoustic wave for the reconstruction of a three-dimensional image. Image reconstruction is a two-step process: In the first step data from a stack of circular integrating are used to reconstruct the circular projection of the source distribution. In the second step the inverse circular Radon transform is appl...

Exact Reconstruction in Photoacoustic Tomography with Circular Integrating Detectors II: Spherical Geometry

Illuminating tissue with pulsed electromagnetic waves generates acoustic waves inside an object which can be measured and converted into a three dimensional (3d) image. This text is concerned with a twostep reconstruction method where the acoustic pressure is measured with circular integrating detectors. In the first step reconstruction formulas for some kind of projection of the source distrib...

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

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. A major breakthrough in the 2D c...

Integrating Detectors for Photoacoustic Imaging

Inversion of the circular Radon transform on an annulus

The representation of a function by its circular Radon transform (CRT) and various related problems arise in many areas of mathematics, physics and imaging science. There has been a substantial spike of interest towards these problems in the last decade mainly due to the connection between the CRT and mathematical models of several emerging medical imaging modalities. This paper contains some n...