In this talk, we will discuss applications of inverse problems arising in imaging, in the light of accessibility to cultural heritage artefacts. With the aim to ease the work of historians and museum curators, as well as to make artefacts more easily accessible to the general public, we emphasize the potential of multimodal image registration, as well as 3D-reconstruction techniques. As an example, we focus in this study on the Bayeux Tapestry, a world-famous medieval wool embroidery included in Unesco's Memory of the World registery. The Tapestry has been an object of investigation, research and hypothesis for almost three centuries. However, researchers and scientists interested in the study of this artefact are confronted with problems related to temporal or geographical constraints i.e., to accessibility. We will first describe some image processing tools which were developed for facilitating the access to the Tapestry to scientists and to the general public. Then, we demonstrate the potential of 3D-reconstruction techniques for virtually relighting it in surface inspection or augmented reality applications, and for realizing high-detail 3D-printed mockups.