  We study an inverse initial source problem that models Photoacoustic
tomography measurements with array detectors, and introduce a method that can
be viewed as a modification of the so called back and forth nudging method. We
show that the method converges at an exponential rate under a natural
visibility condition, with data given only on a part of the boundary of the
domain of wave propagation. In this paper we consider the case of noiseless
measurements.
