Hamilton-Green solver for the forward and adjoint problems in photoacoustic tomography

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Hamilton-Green solver for the forward and adjoint problems in photoacoustic tomography

Rul⋅lan, F; Betcke, MM; (2022) Hamilton-Green solver for the forward and adjoint problems in photoacoustic tomography. Journal of Computational Physics , 449 , Article 110797. 10.1016/j.jcp.2021.110797. Green open access

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Abstract

The majority of the solvers for the acoustic problem in Photoacoustic Tomography (PAT) rely on full solution of the wave equation, which makes them less suitable for real-time and dynamic applications where only partial data is available. This is in contrast to other tomographic modalities, e.g. X-ray tomography, where partial data implies partial cost for the application of the forward and adjoint operators. In this work we present a novel solver for the forward and adjoint wave equations for the acoustic problem in PAT. We term the proposed solver Hamilton-Green as it approximates the fundamental solution to the respective wave equation along the trajectories of the Hamiltonian system resulting from the high frequency asymptotic approximate solution for the wave equation. This approach is flexible and scalable in the sense that it allows computing the solution for each sensor independently at a fraction of the cost of the full wave solution. The theoretical foundations of our approach are rooted in results available in seismics and ocean acoustics. To demonstrate the feasibility of our approach we present results for 2D domains with homogeneous and heterogeneous sound speeds and evaluate them against a full wave solution obtained with a pseudospectral finite difference method implemented in the k-Wave toolbox [1].

Type:	Article
Title:	Hamilton-Green solver for the forward and adjoint problems in photoacoustic tomography
Open access status:	An open access version is available from UCL Discovery
DOI:	10.1016/j.jcp.2021.110797
Publisher version:	https://doi.org/10.1016/j.jcp.2021.110797
Language:	English
Additional information:	This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords:	Photoacoustic tomography, Wave equation, High frequency, Ray tracing, Green’s function
UCL classification:	UCL 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
URI:	https://discovery.ucl.ac.uk/id/eprint/10139959