Hyperspectral images are analytical measurements that provide spatial and structural information. The spatial description of the samples is the specific asset of these measurements and the reason why they have become so important in (bio)chemical fields, where the microdistribution of sample constituents or the morphology or spatial pattern of sample elements constitute very relevant information. Often, because of the small size of the samples, the spatial detail provided by the image acquisition systems is insufficient. This work proposes a data processing strategy to overcome this instrumental limitation and increase the natural spatial detail present in the acquired raw images. The approach works by combining the information of a set of images, slightly shifted from each other with a motion step among them lower than the pixel size of the raw images. The data treatment includes the application of multivariate curve resolution (unmixing) multiset analysis to the set of collected images to obtain the distribution maps and spectral signatures of the sample constituents. These sets of maps are noise-filtered and compound-specific representations of all the relevant information in the pixel space and decrease the dimensionality of the original image from hundreds of spectral channels to few sets of maps, one per sample constituent or element. The information in each compound-specific set of maps is combined via a super-resolution post-processing algorithm, which takes into account the shifting, decimation, and point spread function of the instrument to reconstruct a single map per sample constituent with much higher spatial detail than that of the original image measurement.