  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 asymptotics for the wave equation. This
approach is fast 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. We present results for 2D
numerical phantom with heterogeneous sound speed which we evaluate against a
full wave solution obtained with a pseudospectral method implemented in k-Wave
toolbox.
