Photoacoustic tomography in absorbing acoustic media using time reversal

The reconstruction of photoacoustic images typically neglects the effect of acoustic absorption on the measured time domain signals. Here, a method to compensate for acoustic absorption in photoacoustic tomography is described. The approach is based on time-reversal image reconstruction and an absorbing equation of state which separately accounts for acoustic absorption and dispersion following a frequency power law. Absorption compensation in the inverse problem is achieved by reversing the absorption proportionality coefficient in sign but leaving the equivalent dispersion parameter unchanged. The reconstruction is regularized by filtering the absorption and dispersion terms in the spatial frequency domain using a Tukey window. This maintains the correct frequency dependence of these parameters within the filter pass band. The method is valid in one, two and three dimensions, and for arbitrary power law absorption parameters. The approach is verified through several numerical experiments. The reconstruction of a carbon fibre phantom and the vasculature in the abdomen of a mouse are also presented. When absorption compensation is included, a general improvement in the image magnitude and resolution is seen, particularly for deeper features.