  The unprecedented success of image reconstruction approaches based on deep
neural networks has revolutionised both the processing and the analysis
paradigms in several applied disciplines. In the field of digital humanities,
the task of digital reconstruction of ancient frescoes is particularly
challenging due to the scarce amount of available training data caused by
ageing, wear, tear and retouching over time. To overcome these difficulties, we
consider the Deep Image Prior (DIP) inpainting approach which computes
appropriate reconstructions by relying on the progressive updating of an
untrained convolutional neural network so as to match the reliable piece of
information in the image at hand while promoting regularisation elsewhere. In
comparison with state-of-the-art approaches (based on variational/PDEs and
patch-based methods), DIP-based inpainting reduces artefacts and better adapts
to contextual/non-local information, thus providing a valuable and effective
tool for art historians. As a case study, we apply such approach to reconstruct
missing image contents in a dataset of highly damaged digital images of
medieval paintings located into several chapels in the Mediterranean Alpine Arc
and provide a detailed description on how visible and invisible (e.g.,
infrared) information can be integrated for identifying and reconstructing
damaged image regions.
