  In this paper, we study the photoacoustic tomography problem for which we
seek to recover both the initial state of the pressure field and the wave speed
of the medium from the knowledge of a single boundary measurement. The goal is
to propose practical assumptions to define a set of initial conditions and wave
speeds over which uniqueness for this inverse problem is guaranteed. The main
result of the paper is that given two sets of wave speeds and pressure
profiles, they cannot produce the same acoustic measurements if the relative
difference between the wave speeds is much smaller than the relative difference
between the pressure profiles. Implications for iterative joint-reconstruction
algorithms are discussed.
