A wavelet filter bank which minimizes a novel translation invariantdiscrete uncertainty measure

摘要

We develop a novel measure of joint time-frequency localizationapplicable to equivalence classes of finite-length discrete signals,which are of increasing importance in modern signal and image processingapplications. Like the well-known Heisenberg-Weyl uncertainty principlethat quantifies joint localization for continuous signals, this newmeasure is translation invariant and admits an intuitively satisfyinginterpretation in terms of the statistical variance of signal energy intime or space and in frequency. The new measure is. used to design a newlow-pass wavelet analysis filter with optimal joint localization. Thisnew filter is then used to construct a localized separable 2D discretewavelet transform which is demonstrated on several images of generalinterest in practical applications