Reconstruction of the Optical Absorption Coefficient of a Small Absorber from the Absorbed Energy Density

In photoacoustic imaging, energy absorption causes thermoelastic expansion of optical absorbers, which in turn leads to propagation of a pressure wave. The absorbed energy density can be reconstructed from boundary measurements of the induced pressure wave. However, it is the absorption coefficient, not the absorbed energy, that is a fundamental physiological parameter. The absorbed energy density is the product of the optical absorption coefficient and the light fluence, which is assumed to satisfy the diffusion approximation. Since the fluence depends on the distribution of absorption, the problem of reconstructing the absorption coefficient from the absorbed energy is nonlinear. In this paper, we propose two methods for solving the inverse problem in the context of small-volume absorbers.