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

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].