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  1. Journal of Fourier Analysis and Applications
  2. Journal of Fourier Analysis and Applications : Volume 22
  3. Journal of Fourier Analysis and Applications : Volume 22, Issue 6, December 2016
  4. Cartoon Approximation with $$\alpha $$ -Curvelets
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Journal of Fourier Analysis and Applications : Volume 23
Journal of Fourier Analysis and Applications : Volume 22
Journal of Fourier Analysis and Applications : Volume 22, Issue 6, December 2016
The Bochner–Schoenberg–Eberlein Property for Totally Ordered Semigroup Algebras
Cartoon Approximation with $$\alpha $$ -Curvelets
Geometric Space–Frequency Analysis on Manifolds
Diagonalization of the Finite Hilbert Transform on Two Adjacent Intervals
Boundedness of Multilinear Pseudo-differential Operators on Modulation Spaces
An $$L^1$$ -Estimate for Certain Spectral Multipliers Associated with the Ornstein–Uhlenbeck Operator
Weak-Type Boundedness of the Hardy–Littlewood Maximal Operator on Weighted Lorentz Spaces
Counterexamples to the B-spline Conjecture for Gabor Frames
Journal of Fourier Analysis and Applications : Volume 22, Issue 5, October 2016
Journal of Fourier Analysis and Applications : Volume 22, Issue 4, August 2016
Journal of Fourier Analysis and Applications : Volume 22, Issue 3, June 2016
Journal of Fourier Analysis and Applications : Volume 22, Issue 2, April 2016
Journal of Fourier Analysis and Applications : Volume 22, Issue 1, February 2016
Journal of Fourier Analysis and Applications : Volume 21
Journal of Fourier Analysis and Applications : Volume 20
Journal of Fourier Analysis and Applications : Volume 19
Journal of Fourier Analysis and Applications : Volume 18
Journal of Fourier Analysis and Applications : Volume 17
Journal of Fourier Analysis and Applications : Volume 16
Journal of Fourier Analysis and Applications : Volume 15
Journal of Fourier Analysis and Applications : Volume 14
Journal of Fourier Analysis and Applications : Volume 13
Journal of Fourier Analysis and Applications : Volume 12
Journal of Fourier Analysis and Applications : Volume 11
Journal of Fourier Analysis and Applications : Volume 10
Journal of Fourier Analysis and Applications : Volume 9
Journal of Fourier Analysis and Applications : Volume 8
Journal of Fourier Analysis and Applications : Volume 7
Journal of Fourier Analysis and Applications : Volume 6
Journal of Fourier Analysis and Applications : Volume 5
Journal of Fourier Analysis and Applications : Volume 4
Journal of Fourier Analysis and Applications : Volume 3

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Cartoon Approximation with $$\alpha $$ -Curvelets

Content Provider SpringerLink
Author Grohs, Philipp Keiper, Sandra Kutyniok, Gitta Schäfer, Martin
Copyright Year 2015
Abstract It is well-known that curvelets provide optimal approximations for so-called cartoon images which are defined as piecewise $$C^2$$ -functions, separated by a $$C^2$$ singularity curve. In this paper, we consider the more general case of piecewise $$C^\beta $$ -functions, separated by a $$C^\beta $$ singularity curve for $$\beta \in (1,2]$$ . We first prove a benchmark result for the possibly achievable best N-term approximation rate for this more general signal model. Then we introduce what we call $$\alpha $$ -curvelets, which are systems that interpolate between wavelet systems on the one hand ( $$\alpha = 1$$ ) and curvelet systems on the other hand ( $$\alpha = \frac{1}{2}$$ ). Our main result states that those frames achieve this optimal rate for $$\alpha = \frac{1}{\beta }$$ , up to $$\log $$ -factors.
Starting Page 1235
Ending Page 1293
Page Count 59
File Format PDF
ISSN 10695869
Journal Journal of Fourier Analysis and Applications
Volume Number 22
Issue Number 6
e-ISSN 15315851
Language English
Publisher Springer US
Publisher Date 2015-12-14
Publisher Place New York
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Anisotropic scaling Curvelets Nonlinear approximation Ridgelets Shearlets Sparsity equivalence Wavelets Fourier Analysis Signal,Image and Speech Processing Abstract Harmonic Analysis Approximations and Expansions Partial Differential Equations Mathematical Methods in Physics
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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