The structure of balanced multivariate biorthogonal multiwavelets and dual multiframelets

Abstract. Multiwavelets and multiframelets are of interest in several applications such as numerical algorithms and signal processing, due to their desirable properties such as high smoothness and vanishing moments with relatively small supports of their generating functions and masks. In order to process and represent vector-valued discrete data efficiently and sparsely by a multiwavelet transform, a multiwavelet has to be prefiltered or balanced. Balanced orthonormal univariate multiwavelets and multivariate biorthogonal multiwavelets have been studied and constructed in the literature. Dual multiframelets include (bi)orthogonal multiwavelets as special cases, but their fundamental prefiltering and balancing property hasn't been investigated in the literature yet. In this paper we shall study the balancing property of multivariate multiframelets from the point of view of the discrete multiframelet transform. This approach, to our best knowledge, has not been considered so far in...

• Type: Journal
• Year: 2010
• Where: MOC
• Authors: Bin Han
• Keywords: Balancing Orders, Biorthogonal Multiwavelets, Dual Multiframelets, MOC 2010, Security Privacy