Two-dimensional wreath product group-based image processing

Two-dimensional wreath product group-based image processing

Harmonic analysis is at the heart of much of signal and image processing. This is mainly the harmonic analysis of abelian groups, and ultimately, after sampling, and quantizing, finite abelian groups. Nevertheless, this general group theoretic viewpoint has proved fruitful, yielding a natural group-based multiresolution framework as well as some new and potentially useful nonabelian examples. T...

Image Processing with Wreath Product Groups

A Wreath Product Group Approach to Signal Processing

We propose the use of spectral analysis on certain noncommutative finite groups in digital signal processing, and in particular, image processing. We pay significant attention to groups constructed as wreath products of cyclic groups. Within this large class of groups our approach recovers the DFT, Haar wavelet transform, various multichannel pyramid filter banks and other aspects of multiresol...

A wreath product group approach to signal and image processing .I. Multiresolution analysis

This paper continues the investigation in digital signal processing of spectral analysis on certain non-commutative nite groups|wreath product groups. We describe here the generalization of discrete cyclic convolution to convolution over these groups and show how it reduces to multiplication in the spectral domain. Finite group based convolution is deened in both the spatial and spectral domain...

A wreath product group approach to signal and image processing .II. Convolution, correlation, and applications

This paper continues the investigation of the use of spectral analysis on certain noncommutative nite groups|wreath product groups|in digital signal processing. We describe here the generalization of discrete cyclic convolution to convolution over these groups and show how it reduces to multiplication in the spectral domain. Finite group-based convolution is de ned in both the spatial and spect...