The reconstruction task in photoacoustic tomography can vary a lot depending on measured targets, geometry, and especially the quantity we want to recover. Specifically, as the signal is generated due to the coupling of light and sound by the photoacoustic effect, we have the possibility to recover acoustic as well as optical tissue parameters. This is referred to as quantitative imaging, i.e, correct recovery of physical parameters and not just a qualitative image. In this chapter, we aim to give an overview on established reconstruction techniques in photoacoustic tomography. We start with modelling of the optical and acoustic phenomena, necessary for a reliable recovery of quantitative values. Furthermore, we give an overview of approaches for the tomographic reconstruction problem with an emphasis on the recovery of quantitative values, from direct and fast analytic approaches to computationally involved optimisation based techniques and recent data-driven approaches.

翻译：光声层析成像中的重建任务会因测量目标、几何结构以及特别是待恢复参数的不同而存在显著差异。具体而言，由于信号是通过光声效应中光与声的耦合产生的，我们因此能够同时恢复组织的声学参数和光学参数。这被称为定量成像，即正确恢复物理参数而不仅仅是获得定性图像。本章旨在概述光声层析成像中已建立的重建技术。我们首先从光学和声学现象的建模入手，这是实现定量值可靠恢复的必要基础。此外，我们系统介绍了层析成像重建问题的各类方法，重点阐述了从直接快速的分析方法、计算密集型的基于优化的技术到近期数据驱动方法等不同途径对定量值的恢复。