The Computed Tomography Imaging Spectrometer (CTIS) permits a snapshot acquisition of a hyperspectral cube, through the creation of an image of indirect measurements which is then traditionally used for reconstruction of the cube. This reconstruction step is time-consuming and only yields an approximation of the original cube. Following a compressed learning framework, we compare the performance of a classification task carried out on reconstructed cubes on one hand, directly on the raw images on the other. Regarding the latter case, we propose in particular the use of a new Convolutional Neural Network (CNN) architecture called CTIS-Net, whose architecture is tailored to benefit from the specific structure of CTIS images. Results show a sizable increase compared to classification with a standard architecture and compared to a conventional classification on the reconstructed cubes.