  In this paper we consider a mathematical model for photoacoustic imaging
which takes into account attenuation due to thermodynamic dissipation. The
propagation of acoustic (compressional) waves is governed by a scalar wave
equation coupled to the heat equation for the excess temperature. We seek to
recover the initial acoustic profile from knowledge of acoustic measurements at
the boundary.
  We recognize that this inverse problem is a special case of boundary
observability for a thermoelastic system. This leads to the use of
control/observability tools to prove the unique and stable recovery of the
initial acoustic profile in the weak thermoelastic coupling regime. This
approach is constructive, yielding a solvable equation for the unknown acoustic
profile. Moreover, the solution to this reconstruction equation can be
approximated numerically using the conjugate gradient method. If certain
geometrical conditions for the wave speed are satisfied, this approach is
well--suited for variable media and for measurements on a subset of the
boundary. We also present a numerical implementation of the proposed
reconstruction algorithm.
