Advisors: Ann Dooms, Ingrid Daubechies. Date and location of PhD thesis defense: 13 October 2014, Vrije Universiteit Brussel Recent advances in digital image acquisition methods and the wide range of imaging modalities currently available have triggered museums to digitize their painting collections. Not only is this crucial for archival or dissemination purposes but it also enabled the digital analysis of the painting through its digital image counterpart. It also set in motion a cross-disciplinary collaboration between image analysis specialists, mathematicians, statisticians and art historians that have the common goal to develop algorithms and build a digital toolbox in support of art scholarship. Computer processing of digital images of paintings has become a fast growing and challenging field of research during the last few years. Our contribution to this research domain consists of a set of tools that are based on dimensionality reduction methods, sparse representations and dictionary learning techniques. These tools are used to assist in art related matters such as restoration, conservation, art history, material and structure characterization, authentication, dating and even style analysis. Since paintings are complex structures the analysis of all pictorial layers and the support requires a multimodal set of high-resolution image acquisitions. The presented research can broadly be subdivided into three main fields. The first one is the digital enhancement of painting acquisitions in order to assist the art specialist in his professional assessment of the painting. The second main field of research is the automated detection of cracks within the Ghent Altarpiece, which is meant to help in the delicate matter of the conservation of this exceptional masterpiece but also as guidance during its current campaign of restoration. The last field consists of a set of methods that can be deployed in art forensics. These methods consist of the characterization of canvas, the analysis of multispectral imagery of a painting and even the objective quantification of the style of a particular artist.