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Modelling of uncertainties in ultrasound sensor locations in photoacoustic tomography

Photoacoustic tomography (PAT) is an imaging modality developed during the past few decades. In the inverse problem of PAT, the aim is to estimate the spatial distribution of an initial pressure p0 generated by the photoacoustic effect, when photoacoustic time-series pt measured on the boundary of the imaged target are given. To produce accurate photoacoustic images, the forward model linking p0 to pt has to model the measurement setup and the underlying physics to a sufficient accuracy. Use of an inaccurate model can lead to significant errors in the solution of the inverse problem. In this work, we study the effect and compensation of modelling errors due to uncertainties in ultrasound sensor locations in PAT using Bayesian approximation error modelling. The approach is evaluated with simulated and experimental data using various levels of measurement noise, uncertainties in sensor locations and varying sensor geometries. The results indicate that even small errors in the modelling of ultrasound sensor locations can lead to large errors in the solution of the inverse problem. Furthermore, the magnitude of these errors is affected by the amount of measurement noise and the measurement The modelling errors can, however, be well compensated by the approximation error modelling.