Skip to main content
Cornell University
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arxiv logo > math > arXiv:1101.3638

Help | Advanced Search

arXiv logo
Cornell University Logo

quick links

  • Login
  • Help Pages
  • About

Mathematics > Functional Analysis

arXiv:1101.3638 (math)
[Submitted on 19 Jan 2011]

Title:Sparsity Equivalence of Anisotropic Decompositions

Authors:Gitta Kutyniok
View a PDF of the paper titled Sparsity Equivalence of Anisotropic Decompositions, by Gitta Kutyniok
View PDF
Abstract:Anisotropic decompositions using representation systems such as curvelets, contourlet, or shearlets have recently attracted significantly increased attention due to the fact that they were shown to provide optimally sparse approximations of functions exhibiting singularities on lower dimensional embedded manifolds. The literature now contains various direct proofs of this fact and of related sparse approximation results. However, it seems quite cumbersome to prove such a canon of results for each system separately, while many of the systems exhibit certain similarities. In this paper, with the introduction of the concept of sparsity equivalence, we aim to provide a framework which allows categorization of the ability for sparse approximations of representation systems. This framework, in particular, enables transferring results on sparse approximations from one system to another. We demonstrate this concept for the example of curvelets and shearlets, and discuss how this viewpoint immediately leads to novel results for both systems.
Comments: 20 pages, 4 figures
Subjects: Functional Analysis (math.FA); Numerical Analysis (math.NA)
MSC classes: 42C40 (Primary), 42C15, 65T60, 94A08 (Secondary)
Cite as: arXiv:1101.3638 [math.FA]
  (or arXiv:1101.3638v1 [math.FA] for this version)
  https://doi.org/10.48550/arXiv.1101.3638
arXiv-issued DOI via DataCite

Submission history

From: Gitta Kutyniok [view email]
[v1] Wed, 19 Jan 2011 08:29:14 UTC (703 KB)
Full-text links:

Access Paper:

    View a PDF of the paper titled Sparsity Equivalence of Anisotropic Decompositions, by Gitta Kutyniok
  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
math.FA
< prev   |   next >
new | recent | 2011-01
Change to browse by:
cs
cs.NA
math
math.NA

References & Citations

  • NASA ADS
  • Google Scholar
  • Semantic Scholar
a export BibTeX citation Loading...

BibTeX formatted citation

×
Data provided by:

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)
  • Author
  • Venue
  • Institution
  • Topic

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)
  • About
  • Help
  • contact arXivClick here to contact arXiv Contact
  • subscribe to arXiv mailingsClick here to subscribe Subscribe
  • Copyright
  • Privacy Policy
  • Web Accessibility Assistance
  • arXiv Operational Status
    Get status notifications via email or slack