In this thesis I will exploit the fact that the wavelet representation of hyperspectral data is sparse. Techniques from both atomic decomposition and denoising will be modified and used to make an even sparser representation. Assessment will be done on three datasets. At face value my results are better than those of a baseline study with principal component analysis (PCA), however no formal test supports this claim (the variability of the studies are to high). Formal tests show some improvement in fullfilling model assumptions for my methods. This is all done under the curse of dimensionality (i.e. few trainings samples and many parameters).