Multiresolution and wavelets

Multiresolution and Wavelets

Multiresolution is investigated on the basis of shift-invariant spaces. Given a finitely generated shift-invariant subspace S of L2(IR), let Sk be the 2-dilate of S (k ∈ ZZ). A necessary and sufficient condition is given for the sequence {Sk}k∈Z to form a multiresolution of L2(IR). A general construction of orthogonal wavelets is given, but such wavelets might not have certain desirable propert...

Wavelets and Multiresolution Processing

– Fourier transform used to analyze signals by converting signals into a continuous series of sine and cosine functions, each with a constant frequency and amplitude, and of infinite duration – Real world signals (images) have a finite duration and exhibit abrupt changes in frequency – Wavelet transform converts a signal into a series of wavelets – In theory, signals processed by wavelets can b...

Wavelets and Multiresolution Processing

– Fourier transform used to analyze signals by converting signals into a continuous series of sine and cosine functions, each with a constant frequency and amplitude, and of infinite duration – Real world signals (images) have a finite duration and exhibit abrupt changes in frequency – Wavelet transform converts a signal into a series of wavelets – In theory, signals processed by wavelets can b...

Haar wavelets and multiresolution analysis

Wavelets with Frame Multiresolution Analysis

A frame multiresolution (FMRA for short) orthogonal wavelet is a single-function orthogonal wavelet such that the associated scaling space V0 admits a normalized tight frame (under translations). In this paper, we prove that for any expansive matrix A with integer entries, there exist A-dilation FMRA orthogonal wavelets. FMRA orthogonal wavelets for some other expansive matrix with non integer ...