NDLI: Wavelets from the Loop Scheme

Content Provider	Springer Nature Link
Author	Han, Bin Shen, Zuowei
Copyright Year	2005
Abstract	Anewwavelet-based geometric mesh compression algorithm was developed recently in the area of computer graphics by Khodakovsky, Schröder, and Sweldens in their interesting article [23]. The new wavelets used in [23] were designed from the Loop scheme by using ideas and methods of [26, 27], where orthogonal wavelets with exponential decay and pre-wavelets with compact support were constructed. The wavelets have the same smoothness order as that of the basis function of the Loop scheme around the regular vertices which has a continuous second derivative; the wavelets also have smaller supports than those wavelets obtained by constructions in [26, 27] or any other compactly supported biorthogonal wavelets derived from the Loop scheme (e.g., [11, 12]). Hence, the wavelets used in [23] have a good time frequency localization. This leads to a very efficient geometric mesh compression algorithm as proposed in [23]. As a result, the algorithm in [23] outperforms several available geometric mesh compression schemes used in the area of computer graphics. However, it remains open whether the shifts and dilations of the wavelets form a Riesz basis of L2(ℝ2). Riesz property plays an important role in any wavelet-based compression algorithm and is critical for the stability of any wavelet-based numerical algorithms. We confirm here that the shifts and dilations of the wavelets used in [23] for the regular mesh, as expected, do indeed form a Riesz basis of L2(ℝ2) by applying the more general theory established in this article.
Starting Page	615
Ending Page	637
Page Count	23
File Format	PDF
ISSN	10695869
Journal	Journal of Fourier Analysis and Applications
Volume Number	11
Issue Number	6
e-ISSN	15315851
Language	English
Publisher	Birkhäuser-Verlag
Publisher Date	2005-11-01
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Signal, Image and Speech Processing Abstract Harmonic Analysis Approximations and Expansions Fourier Analysis Partial Differential Equations Applications of Mathematics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Analysis

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