Systematic construction of real lapped tight frame transforms

Aliaksei Sandryhaila, Amina Chebira, Christina Milo, Jelena Kovacevic, Markus Püschel

Research output: Contribution to journalArticle

Abstract

We present a constructive algorithm for the design of real lapped equal-norm tight frame transforms. These transforms can be efficiently implemented through filter banks and have recently been proposed as a redundant counterpart to lapped orthogonal transforms, as well as an infinite-dimensional counterpart to harmonic tight frames. The proposed construction consists of two parts: First, we design a large class of new real lapped orthogonal transforms derived from submatrices of the discrete Fourier transform. Then, we seed these to obtain real lapped tight frame transforms corresponding to tight, equal-norm frames. We identify those frames that are maximally robust to erasures, and show that our construction leads to a large class of new lapped orthogonal transforms as well as new lapped tight frame transforms.

Original languageEnglish (US)
Article number5401080
Pages (from-to)2556-2567
Number of pages12
JournalIEEE Transactions on Signal Processing
Volume58
Issue number5
DOIs
StatePublished - May 1 2010

Fingerprint

Filter banks
Discrete Fourier transforms
Seed

Keywords

  • Bases
  • DFT
  • Filter banks
  • Frames
  • Lapped orthogonal transforms
  • Orthonormal
  • Paraunitary matrices
  • Tight

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

Cite this

Systematic construction of real lapped tight frame transforms. / Sandryhaila, Aliaksei; Chebira, Amina; Milo, Christina; Kovacevic, Jelena; Püschel, Markus.

In: IEEE Transactions on Signal Processing, Vol. 58, No. 5, 5401080, 01.05.2010, p. 2556-2567.

Research output: Contribution to journalArticle

Sandryhaila, A, Chebira, A, Milo, C, Kovacevic, J & Püschel, M 2010, 'Systematic construction of real lapped tight frame transforms', IEEE Transactions on Signal Processing, vol. 58, no. 5, 5401080, pp. 2556-2567. https://doi.org/10.1109/TSP.2010.2041865
Sandryhaila, Aliaksei ; Chebira, Amina ; Milo, Christina ; Kovacevic, Jelena ; Püschel, Markus. / Systematic construction of real lapped tight frame transforms. In: IEEE Transactions on Signal Processing. 2010 ; Vol. 58, No. 5. pp. 2556-2567.
@article{2c74531587e14adb892322cac2b7eb2b,
title = "Systematic construction of real lapped tight frame transforms",
abstract = "We present a constructive algorithm for the design of real lapped equal-norm tight frame transforms. These transforms can be efficiently implemented through filter banks and have recently been proposed as a redundant counterpart to lapped orthogonal transforms, as well as an infinite-dimensional counterpart to harmonic tight frames. The proposed construction consists of two parts: First, we design a large class of new real lapped orthogonal transforms derived from submatrices of the discrete Fourier transform. Then, we seed these to obtain real lapped tight frame transforms corresponding to tight, equal-norm frames. We identify those frames that are maximally robust to erasures, and show that our construction leads to a large class of new lapped orthogonal transforms as well as new lapped tight frame transforms.",
keywords = "Bases, DFT, Filter banks, Frames, Lapped orthogonal transforms, Orthonormal, Paraunitary matrices, Tight",
author = "Aliaksei Sandryhaila and Amina Chebira and Christina Milo and Jelena Kovacevic and Markus P{\"u}schel",
year = "2010",
month = "5",
day = "1",
doi = "10.1109/TSP.2010.2041865",
language = "English (US)",
volume = "58",
pages = "2556--2567",
journal = "IEEE Transactions on Signal Processing",
issn = "1053-587X",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "5",

}

TY - JOUR

T1 - Systematic construction of real lapped tight frame transforms

AU - Sandryhaila, Aliaksei

AU - Chebira, Amina

AU - Milo, Christina

AU - Kovacevic, Jelena

AU - Püschel, Markus

PY - 2010/5/1

Y1 - 2010/5/1

N2 - We present a constructive algorithm for the design of real lapped equal-norm tight frame transforms. These transforms can be efficiently implemented through filter banks and have recently been proposed as a redundant counterpart to lapped orthogonal transforms, as well as an infinite-dimensional counterpart to harmonic tight frames. The proposed construction consists of two parts: First, we design a large class of new real lapped orthogonal transforms derived from submatrices of the discrete Fourier transform. Then, we seed these to obtain real lapped tight frame transforms corresponding to tight, equal-norm frames. We identify those frames that are maximally robust to erasures, and show that our construction leads to a large class of new lapped orthogonal transforms as well as new lapped tight frame transforms.

AB - We present a constructive algorithm for the design of real lapped equal-norm tight frame transforms. These transforms can be efficiently implemented through filter banks and have recently been proposed as a redundant counterpart to lapped orthogonal transforms, as well as an infinite-dimensional counterpart to harmonic tight frames. The proposed construction consists of two parts: First, we design a large class of new real lapped orthogonal transforms derived from submatrices of the discrete Fourier transform. Then, we seed these to obtain real lapped tight frame transforms corresponding to tight, equal-norm frames. We identify those frames that are maximally robust to erasures, and show that our construction leads to a large class of new lapped orthogonal transforms as well as new lapped tight frame transforms.

KW - Bases

KW - DFT

KW - Filter banks

KW - Frames

KW - Lapped orthogonal transforms

KW - Orthonormal

KW - Paraunitary matrices

KW - Tight

UR - http://www.scopus.com/inward/record.url?scp=77951172714&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77951172714&partnerID=8YFLogxK

U2 - 10.1109/TSP.2010.2041865

DO - 10.1109/TSP.2010.2041865

M3 - Article

VL - 58

SP - 2556

EP - 2567

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

SN - 1053-587X

IS - 5

M1 - 5401080

ER -