Optimized Construction of Biorthogonal Spline‐Wavelets
Dana Černá, Václav Finěk · AIP conference proceedings · 2008
The paper is concerned with the construction of wavelet bases on the interval derived from B‐splines. The resulting bases generate multiresolution analyses on the unit interval with the desired number of vanishing wavelet moments for primal and dual wavelets. Inner wavelets are translated and dilated versions of well‐known wavelets designed by Cohen, Daubechies, Feauveau [5] while the construction of boundary wavelets is along the lines of [6]. The disadvantage of popular bases from [6] is their bad condition which cause problems in practical applications. Some modifications which lead to better conditioned bases were proposed in [1, 7, 8, 9, 10]. In this contribution, we further improve the condition of spline‐wavelet bases on the interval. Quantitative properties of these bases are presented.