DOI

The construction of symmetric multiwavelets in the multivariate case with useful in applications properties is a challenging task, mainly due to the complexity of the matrix extension problem. Nevertheless, for the interpolating case, a general technique can be developed. For an appropriate pair of symmetry group H and matrix dilation M and for a given H-symmetric interpolating refinable matrix mask, a method for the construction of H-symmetric dual refinable matrix masks with a preassigned order of sum rule is suggested. Wavelet matrix masks are constructed using a certain explicit matrix extension algorithm, and their symmetry properties are studied via its polyphase components. The resulting multiwavelet systems form dual multiwavelet frames, where wavelet functions have symmetry properties, preassigned order of vanishing moments and preassigned order of the balancing property. Several examples are presented.
Translated title of the contributionМногомерные симметричные интерполяционные двойственные фреймы мультивсплесков
Original languageEnglish
Article number1425
Number of pages27
JournalSymmetry
Volume14
Issue number7
DOIs
StatePublished - 11 Jul 2022

    Research areas

  • symmetry group, multivariate multiwavelet frames, matrix mask, interpolating refinable function vector

    Scopus subject areas

  • Mathematics(all)

ID: 98563138