Biomedical Imaging Group
Logo EPFL
    • Splines Tutorials
    • Splines Art Gallery
    • Wavelets Tutorials
    • Image denoising
    • ERC project: FUN-SP
    • Sparse Processes - Book Preview
    • ERC project: GlobalBioIm
    • The colored revolution of bioimaging
    • Deconvolution
    • SMLM
    • One-World Seminars: Representer theorems
    • A Unifying Representer Theorem
Follow us on Twitter.
Join our Github.
Masquer le formulaire de recherche
Menu
BIOMEDICAL IMAGING GROUP (BIG)
Laboratoire d'imagerie biomédicale (LIB)
  1. School of Engineering STI
  2. Institute IEM
  3.  LIB
  4.  Ideal Filters
  • Laboratory
    • Laboratory
    • Laboratory
    • People
    • Jobs and Trainees
    • News
    • Events
    • Seminars
    • Resources (intranet)
    • Twitter
  • Research
    • Research
    • Researchs
    • Research Topics
    • Talks, Tutorials, and Reviews
  • Publications
    • Publications
    • Publications
    • Database of Publications
    • Talks, Tutorials, and Reviews
    • EPFL Infoscience
  • Code
    • Code
    • Code
    • Demos
    • Download Algorithms
    • Github
  • Teaching
    • Teaching
    • Teaching
    • Courses
    • Student projects
  • Splines
    • Teaching
    • Teaching
    • Splines Tutorials
    • Splines Art Gallery
    • Wavelets Tutorials
    • Image denoising
  • Sparsity
    • Teaching
    • Teaching
    • ERC project: FUN-SP
    • Sparse Processes - Book Preview
  • Imaging
    • Teaching
    • Teaching
    • ERC project: GlobalBioIm
    • The colored revolution of bioimaging
    • Deconvolution
    • SMLM
  • Machine Learning
    • Teaching
    • Teaching
    • One-World Seminars: Representer theorems
    • A Unifying Representer Theorem

On the Optimality of Ideal Filters for Pyramid and Wavelet Signal Approximation

M. Unser

IEEE Transactions on Signal Processing, vol. 41, no. 12, pp. 3591-3596, December 1993.


The reconstructed lowpass component in a quadrature mirror filter (QMF) bank provides a coarser resolution approximation of the input signal. Since the outputs of the two QMF branches are orthogonal, the transformation that provides the maximum energy compaction in the lowpass channel is also the one that results in the minimum approximation error. This property is used as a common strategy for the optimization of QMF banks, orthogonal wavelet transforms, and least squares pyramids. A general solution is derived for the QMF bank that provides the optimal decomposition of an arbitrary wide sense stationary process. This approach is extended to the continuous case to obtain the minimum error approximation of a signal at a given sampling rate. In particular, it is shown that the sine-wavelet transform is optimal for the representation at all scales of signals with non-increasing spectral density.

@ARTICLE(http://bigwww.epfl.ch/publications/unser9304.html,
AUTHOR="Unser, M.",
TITLE="On the Optimality of Ideal Filters for Pyramid and Wavelet
	Signal Approximation",
JOURNAL="{IEEE} Transactions on Signal Processing",
YEAR="1993",
volume="41",
number="12",
pages="3591--3596",
month="December",
note="")

© 1993 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.
  • Laboratory
  • Research
  • Publications
    • Database of Publications
    • Talks, Tutorials, and Reviews
    • EPFL Infoscience
  • Code
  • Teaching
Logo EPFL, Ecole polytechnique fédérale de Lausanne
Emergencies: +41 21 693 3000 Services and resources Contact Map Webmaster email

Follow EPFL on social media

Follow us on Facebook. Follow us on Twitter. Follow us on Instagram. Follow us on Youtube. Follow us on LinkedIn.
Accessibility Disclaimer Privacy policy

© 2023 EPFL, all rights reserved