  A framework for reconstruction of optical diffusion and absorption
coefficients in quantitative photoacoustic tomography is presented. This
framework is based on a Tikhonov-type functional with a regularization term
promoting sparsity of the absorption coefficient and a prior involving a
Kubelka-Munk absorption-diffusion relation that allows to obtain superior
reconstructions. The reconstruction problem is formulated as the minimization
of this functional subject to the differential constraint given by a
photon-propagation model. The solution of this problem is obtained by a fast
and robust sequential quadratic hamiltonian algorithm based on the Pontryagin
maximum principle. Results of several numerical experiments demonstrate that
the proposed computational strategy is able to obtain reconstructions of the
optical coefficients with high contrast and resolution for a wide variety of
objects.
