  Photoacoustic tomography (PAT) is a non-invasive imaging modality that
requires recovering the initial data of the wave equation from certain
measurements of the solution outside the object. In the standard PAT
measurement setup, the used data consist of time-dependent signals measured on
an observation surface. In contrast, the measured data from the recently
invented full-field detection technique provide the solution of the wave
equation on a spatial domain at a single instant in time. While reconstruction
using classical PAT data has been extensively studied, not much is known for
the full field PAT problem. In this paper, we build mathematical foundations of
the latter problem for variable sound speed and settle its uniqueness and
stability. Moreover, we introduce an exact inversion method using time-reversal
and study its convergence. Our results demonstrate the suitability of both the
full field approach and the proposed time-reversal technique for high
resolution photoacoustic imaging.
