Digital Breast Tomosynthesis (DBT) is an X-ray imaging modality enabling the reconstruction of 3D volumes of breasts. DBT is mainly used for cancer screening, and is intended to replace conventional mammography in the coming years. However, DBT reconstructions are impeded by several types of artefacts induced by the geometry of the device itself, degrading the image quality and limiting its resolution along the thickness of the compressed breast. In this study, we propose a deep-learning-based pipeline to address the DBT reconstruction problem, focusing on the removal of sparse-view and limited-angle artefacts. Specifically, this procedure is composed of two steps: a classic reconstruction algorithm is first applied on normalised projections, then a deep neural network is tasked with erasing the artefacts present in the obtained volumes. A major difficulty to solve our problem is the lack of real conditions artefact-free data. To overcome this complication, we resort to a new dataset comprised of synthetic breast texture phantoms. We then show that our training method and database strategy are promising to tackle the problem as they improve the informational value of planes orthogonal to the detector, which are not currently used by radiologists due to their poor quality. Eventually, we assess the impact of removing the bias components from the network and using stacks of slices as inputs, with regard to the generalisation ability of our approach on both synthetic and clinical data.