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.

翻译：提出了一种用于定量光声层析成像中光学扩散系数和吸收系数重建的框架。该框架基于带正则化项的Tikhonov型泛函，正则化项促进吸收系数的稀疏性，并引入基于Kubelka-Munk吸收-扩散关系的先验信息，从而获得更优的重建结果。重建问题被表述为该泛函在光子传播模型微分约束下的最小化问题。通过基于庞特里亚金极大值原理的快速稳健序列二次哈密顿算法求解该问题。多项数值实验结果表明，所提出的计算策略能够对多种目标实现高对比度与高分辨率的光学系数重建。