Automation of the lifting factorisation of wavelet transforms
type: Item
instance of: scholarly article
title: Automation of the lifting factorisation of wavelet transforms
zbMATH Open document ID: 0964.65151
DOI: 10.1016/S0010-4655(99)00451-8
author: M. Maslen
author: Paul C. Abbott
published in: Computer Physics Communications
publication date: 2001-06-26T00:00:00Z
review text: The lifting scheme for finding the discrete wavelet transform depends on the factorization of polyphase matrices, whose entries are Laurent polynomials. Such factorization is not unique. In this paper, the authors outline a Mathematica program that finds all factorizations of such matrices by automating the Euclidean algorithm for Laurent polynomials. Gröbner bases are used to the reduce polynomial degree and the number of wavelet coefficients.
Mathematics Subject Classification ID: 65T60
Mathematics Subject Classification ID: 42C40
zbMATH DE Number: 1485018
zbMATH Keywords: discrete wavelet transform
zbMATH Keywords: lifting scheme
zbMATH Keywords: polyphase matrices
zbMATH Keywords: Laurent polynomials
zbMATH Keywords: Mathematica program
zbMATH Keywords: factorizations
zbMATH Keywords: Euclidean algorithm
zbMATH Keywords: Gröbner bases
reviewed by: Chengshu Wang
describes a project that uses: Mathematica
MaRDI profile type: Publication
Wikidata QID: Q127304917
full work available at URL: s0010-4655(99)00451-8
OpenAlex ID: W1979381854
description: scientific article; zbMATH DE number 1485018