Abstract In the first, theoretical, part of this paper we describe briefly some basic factsabout group theoretical generalizations of the discrete Fourier transform and its connection to the Karhunen Loeve transform. We show that the computation of the eigenvectors and eigenvalues of a covariance matrix can be essentially simplified if the underlying stochastic process possesses a group-theoretically defined symmetry. In the second part of the paper we investigate some properties of a large databases of imagepatches collected from a standard TV-channel and compare the quality of different approximations of the Karhunen-Loeve transform when they are applied to pixel data from the database. We then illustrate the use of non-standard tilings of the image in image coding. The application of DCT-based algorithms is no longer efficient for these tilings, whereas approximations based on dihedral transforms are still possible.