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.  Regularized Reconstruction
  • 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

Continuous-Domain Signal Reconstruction Using Lp-Norm Regularization

P. Bohra, M. Unser

IEEE Transactions on Signal Processing, vol. 68, pp. 4543-4554, August 3, 2020.


We focus on the generalized-interpolation problem. There, one reconstructs continuous-domain signals that honor discrete data constraints. This problem is infinite-dimensional and ill-posed. We make it well-posed by imposing that the solution balances data fidelity and some Lp-norm regularization. More specifically, we consider p ≥ 1 and the multi-order derivative regularization operator L = DN0. We reformulate the regularized problem exactly as a finite-dimensional one by restricting the search space to a suitable space of polynomial splines with knots on a uniform grid. Our splines are represented in a B-spline basis, which results in a well-conditioned discretization. For a sufficiently fine grid, our search space contains functions that are arbitrarily close to the solution of the underlying problem where our constraint that the solution must live in a spline space would have been lifted. This remarkable property is due to the approximation power of splines. We use the alternating-direction method of multipliers along with a multiresolution strategy to compute our solution. We present numerical results for spatial and Fourier interpolation. Through our experiments, we investigate features induced by the Lp-norm regularization, namely, sparsity, regularity, and oscillatory behavior.

@ARTICLE(http://bigwww.epfl.ch/publications/bohra2002.html,
AUTHOR="Bohra, P. and Unser, M.",
TITLE="Continuous-Domain Signal Reconstruction Using $L_{p}$-Norm
	Regularization",
JOURNAL="{IEEE} Transactions on Signal Processing",
YEAR="2020",
volume="68",
number="",
pages="4543--4554",
month="August 3,",
note="")

© 2020 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