Cartoon Approximation with α -Curvelets

Grohs, Philipp; Keiper, Sandra; Kutyniok, Gitta und Schäfer, Martin (2016): Cartoon Approximation with α -Curvelets. In: Journal of Fourier Analysis and Applications, Bd. 22: S. 1235-1293

Abstract

It is well-known that curvelets provide optimal approximations for so-called cartoon images which are defined 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 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 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.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik > Professur für Mathematische Grundlagen des Verständnisses der künstlichen Intelligenz
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 1069-5869
• Sprache: Englisch