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On the Adjoint Operator in Photoacoustic Tomography

Arridge, SR; Betcke, MM; Cox, BT; Lucka, F; Treeby, BE; (2016) On the Adjoint Operator in Photoacoustic Tomography. Inverse Problems , 32 (11) , Article 115012. 10.1088/0266-5611/32/11/115012. Green open access

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Abstract

Photoacoustic tomography (PAT) is an emerging biomedical imaging from coupled physics technique, in which the image contrast is due to optical absorption, but the information is carried to the surface of the tissue as ultrasound pulses. Many algorithms and formulae for PAT image reconstruction have been proposed for the case when a complete data set is available. In many practical imaging scenarios, however, it is not possible to obtain the full data, or the data may be sub-sampled for faster data acquisition. In such cases, image reconstruction algorithms that can incorporate prior knowledge to ameliorate the loss of data are required. Hence, recently there has been an increased interest in using variational image reconstruction. A crucial ingredient for the application of these techniques is the adjoint of the PAT forward operator, which is described in this article from physical, theoretical and numerical perspectives. First, a simple mathematical derivation of the adjoint of the PAT forward operator in the continuous framework is presented. Then, an efficient numerical implementation of the adjoint using a k-space time domain wave propagation model is described and illustrated in the context of variational PAT image reconstruction, on both 2D and 3D examples including inhomogeneous sound speed. The principal advantage of this analytical adjoint over an algebraic adjoint (obtained by taking the direct adjoint of the particular numerical forward scheme used) is that it can be implemented using currently available fast wave propagation solvers.

Type: Article
Title: On the Adjoint Operator in Photoacoustic Tomography
Open access status: An open access version is available from UCL Discovery
DOI: 10.1088/0266-5611/32/11/115012
Publisher version: http://dx.doi.org/10.1088/0266-5611/32/11/115012
Language: English
Additional information: Copyright © 2016 IOP Publishing Ltd. Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence (http://creativecommons.org/licenses/by/3.0/). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Med Phys and Biomedical Eng
URI: http://discovery.ucl.ac.uk/id/eprint/1489763
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