Spectral analysis of mosaics

Abstract

Two-sided spectra of patterns based on classes of orthogonal matrices are introduced and their main properties are discussed. In particular, the "mosaicness" of patterns is studied. Some effects of noise on mosaics can effectively be analyzed in the spectral domain. The mosaic structure of patterns can easily be recognized in the spectral domain, albeit the mosaic structure cannot always be unambiguously determined. 2D-Dirichlet kernels based on non-Abelian groups may however be used for a more efficient analysis of mosaics.