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Continuous Shearlet Tight Frames

Grohs, Philipp

In: Journal of Fourier Analysis and Applications, 2011, vol. 17, no. 3, p. 506-518

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    Titre
    • Continuous Shearlet Tight Frames
    Auteur
    • Grohs, Philipp. Seminar for Applied Mathematics, ETH Zürich, Rämistraße 101, 8092, Zürich, Switzerland
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Journal of Fourier Analysis and Applications, 2011, vol. 17, no. 3, p. 506-518. SP Birkhäuser Verlag Boston
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:318465
    Summary
    Based on the shearlet transform we present a general construction of continuous tight frames for L 2(ℝ2) from any sufficiently smooth function with anisotropic moments. This includes for example compactly supported systems, piecewise polynomial systems, or both. From our earlier results in Grohs (Technical report, KAUST, 2009) it follows that these systems enjoy the same desirable approximation properties for directional data as the previous bandlimited and very specific constructions due to Kutyniok and Labate (Trans. Am. Math. Soc. 361:2719-2754, 2009). We also show that the representation formulas we derive are in a sense optimal for the shearlet transform