Single-stage reconstruction algorithm for quantitative photoacoustic tomography

The development of efficient and accurate image reconstruction algorithms is one of the cornerstones of computed tomography. Existing algorithms for quantitative photoacoustic tomography (qPAT) 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 qPAT, where the optical parameters are directly reconstructed from the observed acoustical data. In that context we formulate the image reconstruction problem of qPAT 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.