Appears in collection : Mathematical and numerical approaches for multi-wave inverse problems / Approches mathématiques et numériques pour les problèmes inverses de type multi-ondes

​We consider photoacoustic tomography in the presence of approximation and modelling errors. The inverse problem, i.e. estimation of the initial pressure from photoacoustic time-series measured on the boundary of the target, is approached in the framework of Bayesian inverse problems. The posterior distribution is examined in situations in which the forward model contains errors or uncertainties for example due to numerical approximations or uncertainties in the acoustic parameters. Modelling of these errors and its impact on the posterior distribution are investigated. This is joint work with Teemu Sahlstrm, Jenni Tick and Aki Pulkkinen.