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Orthonormal Compactly Supported Wavelets with Optimal Sobolev Regularity

Harri Ojanen
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Abstract

Numerical optimization is used to construct new orthonormal compactly supported wavelets with Sobolev regularity exponent as high as possible among those mother wavelets with a fixed support length and a fixed number of vanishing moments. The increased regularity is obtained by optimizing the locations of the roots the scaling filter has on the interval (pi/2,π). The results improve those obtained by I. Daubechies [Comm. Pure Appl. Math. 41 (1988), 909-996], H. Volkmer [SIAM J. Math. Anal. 26 (1995), 1075-1087], and P. G. Lemarie-Rieusset and E. Zahrouni [Appl. Comput. Harmon. Anal. 5 (1998), 92-105].

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Harri Ojanen. 1998-07-16. Orthonormal Compactly Supported Wavelets with Optimal Sobolev Regularity. https://arxiv.org/abs/math/9807089

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