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https://doi.org/10.1007/s00041-005-5013-x
DC Field | Value | |
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dc.title | Wavelets from the loop scheme | |
dc.contributor.author | Han, B. | |
dc.contributor.author | Shen, Z. | |
dc.contributor.author | Cohen, A. | |
dc.date.accessioned | 2014-10-28T02:49:40Z | |
dc.date.available | 2014-10-28T02:49:40Z | |
dc.date.issued | 2005-12 | |
dc.identifier.citation | Han, B., Shen, Z., Cohen, A. (2005-12). Wavelets from the loop scheme. Journal of Fourier Analysis and Applications 11 (6) : 615-637. ScholarBank@NUS Repository. https://doi.org/10.1007/s00041-005-5013-x | |
dc.identifier.issn | 10695869 | |
dc.identifier.uri | http://scholarbank.nus.edu.sg/handle/10635/104463 | |
dc.description.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. © 2005 Birkhäuser Boston. All rights reserved. | |
dc.description.uri | http://libproxy1.nus.edu.sg/login?url=http://dx.doi.org/10.1007/s00041-005-5013-x | |
dc.source | Scopus | |
dc.subject | Box splines | |
dc.subject | High-dimensional Riesz wavelet bases | |
dc.subject | Wavelets from the Loop scheme | |
dc.type | Article | |
dc.contributor.department | MATHEMATICS | |
dc.description.doi | 10.1007/s00041-005-5013-x | |
dc.description.sourcetitle | Journal of Fourier Analysis and Applications | |
dc.description.volume | 11 | |
dc.description.issue | 6 | |
dc.description.page | 615-637 | |
dc.identifier.isiut | 000234544400001 | |
Appears in Collections: | Staff Publications |
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