Irregular Filters for Semi-regular Dubuc-Deslauriers Wavelet Tight Frames

Viscardi, Alberto

doi:10.17632/f5rc39k9m4.1

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“…Thus, by (31) and the second identity in (34), Rm α = 0. Since, by Proposition 4.3 and (29), we have R k m α = 0, k ∈ I irr , due to (30), we obtain…”

Section: Semi-regular Dubuc-deslauriers Wavelet Tight Framementioning

confidence: 97%

“…(ii) In the irregular case, due to the special structure of S and (33) from the regular case, the identity (31) reduces to an identity for certain finite matrices. For m α in (23) and c α in ( 16), α = 0, .…”

Section: Semi-regular Dubuc-deslauriers Wavelet Tight Framementioning

confidence: 99%

“…For the interested reader, the irregular filters Q irr for n = 2, 3, 4, 5 and several values of h r > 0 are available in [31].…”

Section: Examplesmentioning

confidence: 99%

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Semi-regular Dubuc–Deslauriers wavelet tight frames

Viscardi

2019

Journal of Computational and Applied Mathematics

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In this paper, we construct wavelet tight frames with n vanishing moments for Dubuc-Deslauriers 2npoint semi-regular interpolatory subdivision schemes. Our motivation for this construction is its practical use for further regularity analysis of wide classes of semi-regular subdivision. Our constructive tools are local eigenvalue convergence analysis for semi-regular Dubuc-Deslauriers subdivision, the Unitary Extension Principle and the generalization of the Oblique Extension Principle to the irregular setting by Chui, He and Stöckler. This group of authors derives suitable approximation of the inverse Gramian for irregular Bspline subdivision. Our main contribution is the derivation of the appropriate approximation of the inverse Gramian for the semi-regular Dubuc-Deslauriers scaling functions ensuring n vanishing moments of the corresponding framelets.

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“…Thus, by (31) and the second identity in (34), Rm α = 0. Since, by Proposition 4.3 and (29), we have R k m α = 0, k ∈ I irr , due to (30), we obtain…”

Section: Semi-regular Dubuc-deslauriers Wavelet Tight Framementioning

confidence: 97%

Section: Semi-regular Dubuc-deslauriers Wavelet Tight Framementioning

confidence: 99%