Photoacoustic tomography (PAT) holds great promise as a medical imaging tool, for rendering high-resolution images of vasculature and blood oxygenation in tissue, non-invasively and at a low computational expense. In this project, we look at the reconstruction of 2D cross-sections of small animals, from cylindrically focused ultrasound transducers arranged in a circle around the animal. The transducers are focused to receive ultrasound from the cross-section, in order to perform a quick reconstruction in two dimensions. However, sources positioned near the cross-section will also be picked up by the transducers, so-called out-of-plane contributions, which results in artefacts, and a significantly low resolution across the different cross-sections. To correct for the out-of-plane contributions, we look at a variety of mathematical reconstruction techniques, such as regularisation methods, deconvolution methods and modelling the inverse problem in three dimensions. We are also interested in super-resolution processing as a means of improving the image quality post-reconstruction.