Preliminaries

Abstract

This chapter introduces the concepts that are the main subject of the rest of this work, along with the essential tools that are needed. After a brief introduction on harmonic analysis in non-commutative groups, we introduce the general setting considered in this work, alongside with some essential facts on its representation theory. Afterwards, we recall some basic notions on almost-periodic functions and and a precise construction that allows to select some relevant subspaces. Finally we present our models for natural images (compactly supported functions of and textures (properly selected finite-dimensional subspaces of almost-periodic functions in the plane).