Single-stage reconstruction algorithm for quantitative photoacoustic tomography. (7th May 2015) - Haltmeier, Markus; Neumann, Lukas; Rabanser, Simon
Abstract: 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.