This research program deals with the quality enhancement of digital images. Specifically, we consider the increasingly common situations where several acquisitions of the same scene are available, possibly through a video sequence. An issue of growing importance is to fuse these images in order to get a single enhanced image. Another crucial question concerns the joint restoration of several images of the same sequence. Such an approach has two great advantages. First, going beyond the physical limitations of sensors becomes possible, in terms of dynamic range, resolution or signal- to-noise ratio. Second, the classical limitations of single shot imaging (blur, specular reflections, over or under-exposure, etc.) may be strongly attenuated. As a counterpart, multi-image restoration faces specific difficulties, the toughest of which are related to change detection, motion detection, outliers (aberrant pixels or regions) detection, inpainting, contrast and colour corrections. The proposed work program gathers several classical problems from image processing together with complex issues in image analysis and comparisons. It builds on various mathematical tools, mainly statistical estimation, optimization, stochastic modeling, variational approaches and optimal transport. Within this program, our main goal will be to develop reliable and efficient numerical algorithms for each of the studied restoration modalities.