Photoacoustic and Coupled Physics Imaging

There exist various reconstruction formulas and back-projection algorithms for photoacoustic imaging (see the survey [4] and the references therein). Also different measurement devices for the ultrasound pressure have been suggested. Most common are small detectors based on materials, which exhibit a strong piezoelectric effect and can be immersed safely in water (i.e. polymers such as PVDF). In analytical reconstruction formulas, they are considered point detectors. Other experimental setups have been realized with line and area detectors, which collect averaged pressure (see [9] for a survey). Here, we consider the problem of photoacoustic sectional imaging. Opposed to standard photoacoustic imaging, where the detectors record sets of two-dimensional projection images from which the three-dimensional imaging data can be reconstructed, single slice imaging reconstructs a set of two-dimensional slices, each by a single scan procedure. The advantages of the latter approach are a considerable increase in measurement speed and the possibility to do selective plane imaging. In general, this can only be obtained by the cost of decreased out-of-plane resolution. The difference in this model to previously studied models is that the wave propagation is considered fully three-dimensional, the initialization and measurements are fully two-dimensional due to the selective plane illumination and detection. Therefore, such setups require novel reconstruction formulas, which have been explained in this talk. After the introduction of the universal back-projection algorithm introduced in [11] this goal seems superfluous. However, it has been shown recently by Natterer [6] that universal back-projection is only exact for special sampling geometries. Here, for sliced imaging and certain sampling setups, we can indeed find mathematically exact universal reconstruction algorithms for arbitrary strictly convex sampling domains Ω. We model the sectional photoacoustic imaging by assuming that the initial pressure distribution f : R → R is perfectly focused in the illumination plane {x ∈ R | x3 = 0}: