Wavelet Analysis as an Information Processing Technique

TL;DR

This paper introduces a novel interpretation of wavelet analysis as an information processing method, establishing a wavelet information theory that quantifies information content and mutual information between signals and wavelets.

Contribution

It proposes a new wavelet information theory framework, defining wavelet entropy and mutual information, and demonstrates how to compute information from multiresolution analysis.

Findings

Wavelet entropy can be defined using associated probability densities.

Wavelet mutual information quantifies the shared information between signals and wavelets.

The framework applies to both continuous and discrete signals.

Abstract

A new interpretation for the wavelet analysis is reported, which can is viewed as an information processing technique. It was recently proposed that every basic wavelet could be associated with a proper probability density, allowing defining the entropy of a wavelet. Introducing now the concept of wavelet mutual information between a signal and an analysing wavelet fulfils the foundations of a wavelet information theory (WIT). Both continuous and discrete time signals are considered. Finally, we showed how to compute the information provided by a multiresolution analysis by means of the inhomogeneous wavelet expansion. Highlighting ideas behind the WIT are presented.