Abstract
Numerical optimization is used to construct new orthonormal compactly supported wavelets with a 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 (π/2,π). The results improve those obtained by I. Daubechies (1988, Comm. Pure Appl. Math. 41, 909–996), H. Volkmer (1995, SIAM J. Math. Anal. 26, 1075–1087), and P. G. Lemarié-Rieusset and E. Zahrouni (1998, Appl. Comput. Harmon. Anal. 5, 92–105).
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