  The development of efficient and accurate image reconstruction algorithms is
one of the cornerstones of computed tomography. Existing algorithms for
quantitative photoacoustic tomography currently operate in a two-stage
procedure: First an inverse source problem for the acoustic wave propagation is
solved, whereas in a second step the optical parameters are estimated from the
result of the first step. Such an approach has several drawbacks. In this paper
we therefore propose the use of single-stage reconstruction algorithms for
quantitative photoacoustic tomography, where the optical parameters are
directly reconstructed from the observed acoustical data. In that context we
formulate the image reconstruction problem of quantitative photoacoustic
tomography as a single nonlinear inverse problem by coupling the radiative
transfer equation with the acoustic wave equation. The inverse problem is
approached by Tikhonov regularization with a convex penalty in combination with
the proximal gradient iteration for minimizing the Tikhonov functional. We
present numerical results, where the proposed single-stage algorithm shows an
improved reconstruction quality at a similar computational cost.

Analysis of PDEs