Photoacoustic tomography is an imaging modality based on the photoacoustic effect caused by the absorption of an externally introduced light pulse. In the inverse problem of photoacoustic tomography, the initial pressure generated through the photoacoustic effect is estimated from a measured photoacoustic time-series utilizing a forward model for ultrasound propagation. Due to the ill-posedness of the inverse problem, errors in the forward model or measurements can result in significant errors in the solution of the inverse problem. In this work, we study modeling of errors caused by uncertainties in ultrasound sensor locations in photoacoustic tomography using a Bayesian framework. The approach is evaluated with simulated and experimental data. The results indicate that the inverse problem of photoacoustic tomography is sensitive even to small uncertainties in sensor locations. Furthermore, these uncertainties can lead to significant errors in the estimates and reduction of the quality of the photoacoustic images. In this work, we show that the errors due to uncertainties in ultrasound sensor locations can be modeled and compensated using Bayesian approximation error modeling. Index Terms Photoacoustic tomography (PAT), inverse problems, Bayesian methods, error modeling.

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Photoacoustic tomography (PAT) is an imaging modality that utilizes the photoacoustic effect. In PAT, a photoacoustic image is computed from measured data by modeling ultrasound propagation in the imaged domain and solving an inverse problem utilizing a discrete forward operator. However, in realistic measurement geometries with several ultrasound transducers and relatively large imaging volume, an explicit formation and use of the forward operator can be computationally prohibitively expensive. In this work, we propose a transformation based approach for efficient modeling of photoacoustic signals and reconstruction of photoacoustic images. In the approach, the forward operator is constructed for a reference ultrasound transducer and expanded into a general measurement geometry using transformations that map the formulated forward operator in local coordinates to the global coordinates of the measurement geometry. The inverse problem is solved using a Bayesian framework. The approach is evaluated with numerical simulations and experimental data. The results show that the proposed approach produces accurate three-dimensional photoacoustic images with a significantly reduced computational cost both in memory requirements and in time. In the studied cases, depending on the computational factors such as discretization, over 30-fold reduction in memory consumption and was achieved without a reduction in image quality compared to a conventional approach.

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 p 0 generated by the photoacoustic effect, when photoacoustic time-series p t measured on the boundary of the imaged target are given. To produce accurate photoacoustic images, the forward model linking p 0 to p t 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 geometry. The modelling errors can, however, be well compensated by the approximation error modelling.