Communications in Mathematical Sciences

Volume 7 (2009)

Number 3

Exact series reconstruction in photoacoustic tomography with circular integrating detectors

Pages: 665 – 678

DOI: http://dx.doi.org/10.4310/CMS.2009.v7.n3.a8

Authors

Markus Haltmeier

Otmar Scherzer

Gerhard Zangerl

Abstract

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 detectors are used to reconstruct the circular projection of the source distribution. In the second step the inverse circular Radon transform is applied. In this article we establish inversion formulas for the first step, which involves an inverse problem for the axially symmetric wave equation. Numerical results are presented that show the validity and robustness of the resulting algorithm.

Keywords

Radon transform; photoacoustic tomography; photoacoustic microscopy; Hankel transform; image reconstruction; integrating detectors; axially symmetric; wave equation

2010 Mathematics Subject Classification

35L05, 44A12, 65R32, 92C55

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