High balanced biorthogonal multiwavelets with symmetry
Summary: Balanced multiwavelet transform can process the vector-valued data sparsely while preserving a polynomial signal. In [Sci. China, Ser. F 49, No. 4, 504--515 (2006; Zbl 1129.42019); Sci. China, Ser. A 49, No. 1, 86--97 (2006; Zbl 1193.42100)], \textit{S. Yang} and \textit{L. Peng} constructed balanced multiwavelets from the existing nonbalanced ones. It will be proved, however, in this paper that if the nonbalanced multiwavelets have antisymmetric component, it is impossible for the balanced multiwavelets by the method mentioned above to have symmetry. In this paper, we give an algorithm for constructing a pair of biorthogonal symmetric refinable function vectors from any orthogonal refinable function vector, which has symmetric and antisymmetric components. Then, a general scheme is given for high balanced biorthogonal multiwavelets with symmetry from the constructed pair of biorthogonal refinable function vectors. Moreover, we discuss the approximation orders of the biorthogonal symmetric refinable function vectors. An example is given to illustrate our results.
scientific article; zbMATH DE number 7021821