Quantitative Photoacoustic Tomography with Piecewise Constant Material Parameters

The goal of quantitative photoacoustic tomography is to determine optical and acoustical material properties from initial pressure maps such as those obtained, for instance, from photoacoustic imaging. The most relevant parameters are absorption, diffusion, and Grüneisen coefficients, all of which can be heterogeneous. Recent work by Bal and Ren shows that, in general, unique reconstruction of all three parameters is impossible, even if multiple measurements of the initial pressure (corresponding to different laser excitation directions at a single wavelength) are available. Here, we propose a restriction to piecewise constant material parameters. We show that in the diffusion approximation of light transfer, piecewise constant absorption, diffusion, and Grüneisen coefficients can be recovered uniquely from photoacoustic measurements at a single wavelength. In addition, we implemented our ideas numerically and tested them on simulated three-dimensional data.