Communications in Mathematical Sciences

Exact series reconstruction in photoacoustic tomography with circular integrating detectors

Gerhard Zangerl, Otmar Scherzer, and Markus Haltmeier

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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.

Article information

Commun. Math. Sci., Volume 7, Number 3 (2009), 665-678.

First available in Project Euclid: 26 October 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 44A12: Radon transform [See also 92C55] 65R32: Inverse problems 35L05: Wave equation 92C55: Biomedical imaging and signal processing [See also 44A12, 65R10, 94A08, 94A12]

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


Zangerl, Gerhard; Scherzer, Otmar; Haltmeier , Markus. Exact series reconstruction in photoacoustic tomography with circular integrating detectors. Commun. Math. Sci. 7 (2009), no. 3, 665--678.

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