Two-dimensional wreath product group-based image processing

A theoretical foundation to the notion of 2D transform and 2D signal processing is given, focusing on 2D group-based transforms, of which the 2D Haar and 2D Fourier transforms are particular instances. Conditions for separability of these transforms are established. The theory is applied to certain groups that are wreath products of cyclic groups to give separable and inseparable 2D wreath product transforms and their filter bank implementations.