Scaling laplacian pyramids

Youngmi Hur, Kasso A. Okoudjou

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Laplacian pyramid-based Laurent polynomial (LP2) matrices are generated by Laurent polynomial column vectors and have long been studied in connection with Laplacian pyramidal algorithms in signal processing. In this paper, we investigate when such matrices are scalable, that is, when right multiplication by Laurent polynomial diagonal matrices results in paraunitary matrices. The notion of scalability has recently been introduced in the context of finite frame theory and can be considered as a preconditioning method for frames. This paper significantly extends the current research on scalable frames to the setting of polyphase representations of filter banks. Furthermore, as applications of our main results we propose new construction methods for tight wavelet filter banks and tight wavelet frames.

Original languageEnglish
Pages (from-to)348-365
Number of pages18
JournalSIAM Journal on Matrix Analysis and Applications
Volume36
Issue number1
DOIs
Publication statusPublished - 2015 Jan 1

Fingerprint

Laurent Polynomials
Pyramid
Polynomial Matrices
Filter Banks
Scaling
Column vector
Wavelet Frames
Tight Frame
Diagonal matrix
Preconditioning
Signal Processing
Scalability
Multiplication
Wavelets

All Science Journal Classification (ASJC) codes

  • Analysis

Cite this

Hur, Youngmi ; Okoudjou, Kasso A. / Scaling laplacian pyramids. In: SIAM Journal on Matrix Analysis and Applications. 2015 ; Vol. 36, No. 1. pp. 348-365.
@article{56a8ff9ff5674ffcad719b121d5583b3,
title = "Scaling laplacian pyramids",
abstract = "Laplacian pyramid-based Laurent polynomial (LP2) matrices are generated by Laurent polynomial column vectors and have long been studied in connection with Laplacian pyramidal algorithms in signal processing. In this paper, we investigate when such matrices are scalable, that is, when right multiplication by Laurent polynomial diagonal matrices results in paraunitary matrices. The notion of scalability has recently been introduced in the context of finite frame theory and can be considered as a preconditioning method for frames. This paper significantly extends the current research on scalable frames to the setting of polyphase representations of filter banks. Furthermore, as applications of our main results we propose new construction methods for tight wavelet filter banks and tight wavelet frames.",
author = "Youngmi Hur and Okoudjou, {Kasso A.}",
year = "2015",
month = "1",
day = "1",
doi = "10.1137/140988231",
language = "English",
volume = "36",
pages = "348--365",
journal = "SIAM Journal on Matrix Analysis and Applications",
issn = "0895-4798",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "1",

}

Scaling laplacian pyramids. / Hur, Youngmi; Okoudjou, Kasso A.

In: SIAM Journal on Matrix Analysis and Applications, Vol. 36, No. 1, 01.01.2015, p. 348-365.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Scaling laplacian pyramids

AU - Hur, Youngmi

AU - Okoudjou, Kasso A.

PY - 2015/1/1

Y1 - 2015/1/1

N2 - Laplacian pyramid-based Laurent polynomial (LP2) matrices are generated by Laurent polynomial column vectors and have long been studied in connection with Laplacian pyramidal algorithms in signal processing. In this paper, we investigate when such matrices are scalable, that is, when right multiplication by Laurent polynomial diagonal matrices results in paraunitary matrices. The notion of scalability has recently been introduced in the context of finite frame theory and can be considered as a preconditioning method for frames. This paper significantly extends the current research on scalable frames to the setting of polyphase representations of filter banks. Furthermore, as applications of our main results we propose new construction methods for tight wavelet filter banks and tight wavelet frames.

AB - Laplacian pyramid-based Laurent polynomial (LP2) matrices are generated by Laurent polynomial column vectors and have long been studied in connection with Laplacian pyramidal algorithms in signal processing. In this paper, we investigate when such matrices are scalable, that is, when right multiplication by Laurent polynomial diagonal matrices results in paraunitary matrices. The notion of scalability has recently been introduced in the context of finite frame theory and can be considered as a preconditioning method for frames. This paper significantly extends the current research on scalable frames to the setting of polyphase representations of filter banks. Furthermore, as applications of our main results we propose new construction methods for tight wavelet filter banks and tight wavelet frames.

UR - http://www.scopus.com/inward/record.url?scp=84983335705&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84983335705&partnerID=8YFLogxK

U2 - 10.1137/140988231

DO - 10.1137/140988231

M3 - Article

AN - SCOPUS:84983335705

VL - 36

SP - 348

EP - 365

JO - SIAM Journal on Matrix Analysis and Applications

JF - SIAM Journal on Matrix Analysis and Applications

SN - 0895-4798

IS - 1

ER -