Wavelets Generated by Vector Multiresolution Analysis

Characterization of Riesz bases of wavelets generated from multiresolution analysis

We investigate Riesz bases of wavelets generated from multiresolution analysis. This investigation leads us to a study of refinement equations with masks being exponentially decaying sequences. In order to study such refinement equations we introduce the cascade operator and the transition operator. It turns out that the transition operator associated with an exponentially decaying mask is a co...

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 ...

Haar wavelets and multiresolution analysis

Multiresolution Document Analysis with Wavelets

The n-gram analysis technique breaks up a text document into several n-character long unique grams, and produces a vector whose components are the counts of these grams. A typical corpus contains hundreds of thousands of such grams. Wavelet compression reduces the dimension of the n-gram vectors, and speeds up document query operations. Document vectors with their dimensions reduced to four com...

Matrix–valued Wavelets and Multiresolution Analysis

We introduce the notions of matrix–valued wavelet set and matrix– valued multiresolution analysis (A-MMRA) associated with a fixed dilation given by an expansive linear map A : R → R, d ≥ 1 such that A(Z) ⊂ Z, in a matrix–valued function space L(R,C), n ≥ 1. These are generalizations of the corresponding notions defined by Xia and Suter in 1996 for the case where d = 1 and A is the dyadic dilat...