Omnidirectional images represent a special type of images that are captured by vision sensors with a 360-degree field of view. This work targets the compression of such images by taking into account their particular geometry. We first map omnidirectional images to spherical ones and then perform sparse image decomposition over a dictionary of geometric atoms on the 2D sphere. A coder based on Matching Pursuit and adaptive quantization is finally proposed for efficient compression of the omnidirectional images. The experiments demonstrate that proposed system outperforms the JPEG2000 coding of unfolded images. As most of omnidirectional sensors can be parametrized with a spherical camera model, the proposed method is generic with respect to different sensor constructions.