Analytical and mathematical methods for revealing hidden details in ancient manuscripts and paintings: A review

[Display omitted] •Methods for revealing hidden details in ancient manuscripts and paintings are presented.•Different experimental approaches are described.•The most effective techniques of image analysis are introduced.•Special attention is given to multi-spectral imaging and blind separation methods.•Several case studies are presented. In this work, a critical review of the current nondestructive probing and image analysis approaches is presented, to revealing otherwise invisible or hardly discernible details in manuscripts and paintings relevant to cultural heritage and archaeology. Multispectral imaging, X-ray fluorescence, Laser-Induced Breakdown Spectroscopy, Raman spectroscopy and Thermography are considered, as techniques for acquiring images and spectral image sets; statistical methods for the analysis of these images are then discussed, including blind separation and false colour techniques. Several case studies are presented, with particular attention dedicated to the approaches that appear most promising for future applications. Some of the techniques described herein are likely to replace, in the near future, classical digital photography in the study of ancient manuscripts and paintings.