Hyperspectral imaging systems provide dense spectral information on the scene under investigation by collecting data from a high number of contiguous bands of the electromagnetic spectrum. The low spatial resolutions of these sensors frequently give rise to the mixing problem in remote sensing applications. Several unmixing approaches are developed in order to handle the challenging mixing problem on perspective images. On the other hand, omnidirectional imaging systems provide a 360-degree field of view in a single image at the expense of lower spatial resolution. In this study, we propose a novel imaging system which integrates hyperspectral cameras with mirrors so on to yield catadioptric omnidirectional imaging systems to benefit from the advantages of both modes. Catadioptric images, incorporating a camera with a reflecting device, introduce radial warping depending on the structure of the mirror used in the system. This warping causes a non-uniformity in the spatial resolution which further complicates the unmixing problem. In this context, a novel spatial-contextual unmixing algorithm specifically for the large field of view of the hyperspectral imaging system is developed. The proposed algorithm is evaluated on various real-world and simulated cases. The experimental results show that the proposed approach outperforms compared methods.