  This paper presents a numerical study on a fast marching method based back
projection reconstruction algorithm for photoacoustic tomography in
heterogeneous media. Transcranial imaging is used here as a case study. To
correct for the phase aberration from the heterogeneity (i.e., skull), the fast
marching method is adopted to compute the phase delay based on the known speed
of sound distribution, and the phase delay is taken into account by the back
projection algorithm for more accurate reconstructions. It is shown that the
proposed algorithm is more accurate than the conventional back projection
algorithm, but slightly less accurate than the time reversal algorithm
particularly in the area close to the skull. However, the image reconstruction
time for the proposed algorithm can be as little as 124 ms when implemented by
a GPU (512 sensors, 21323 pixels reconstructed), which is two orders of
magnitude faster than the time reversal reconstruction. The proposed algorithm,
therefore, not only corrects for the phase aberration, but can be also
potentially implemented in a real-time manner.
