A Hybrid Reconstruction Method for Quantitative PAT

The objective of quantitative photoacoustic tomography (qPAT) is to reconstruct the diffusion and absorption properties of a medium from data of absorbed energy distribution inside the medium. Mathematically, qPAT can be formulated as an inverse coefficient problem for the diffusion equation. Past research showed that if the boundary values of the coefficients are known, then the interior values of the coefficients can be uniquely and stably reconstructed with two well-chosen data sets. We propose a hybrid numerical reconstruction procedure for qPAT that uses both interior energy data and boundary current data, which is usually available in diffuse optical tomography. We show that these data allow the unique reconstruction of the boundary and interior values of the coefficients. The numerical implementation is based on reformulating the inverse coefficient problem as a nonlinear optimization problem. An explicit reconstruction scheme is utilized to eliminate the unknown coefficients inside the medium so that we only need to minimize over the boundary values, which significantly fewer degrees of freedom. Numerical simulations with synthetic data are presented to validate the method.