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Main Title: Cartoon Approximation with α-Curvelets
Author(s): Grohs, Philipp
Keiper, Sandra
Kutyniok, Gitta
Schäfer, Martin
Type: Research Paper
Abstract: It is well-known that curvelets provide optimal approximations for so-called cartoon images which are defi ned as piecewise C2-functions, separated by a C2 singularity curve. In this paper, we consider the more general case of piecewise Cβ-functions, separated by a Cβ singularity curve for β (1;2]. We fi rst 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 α-curvelets, which are systems that interpolate between wavelet systems on the one hand (α = 1) and curvelet systems on the other hand (α= 1/2). Our main result states that those frames achieve this optimal rate for α = 1/β, up to log-factors.
Subject(s): wavelets
rate of convergence
degree of approximation
cartoon approximation
Issue Date: 10-Oct-2014
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 42C40 Wavelets
41A25 Rate of convergence, degree of approximation
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2014, 23
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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