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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 \(L^2({\mathbb R}^2)\)) and textures (properly selected finite-dimensional subspaces of almost-periodic functions in the plane).

Keywords

Harmonic analysis Chu duality Maximally almost periodic groups 

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Laboratoire des Signaux et des SystèmesCéntraleSupelecGif sur YvetteFrance
  2. 2.LSISUniversité de ToulonLa Garde CedexFrance

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